Science.gov

Sample records for geometry reconstrucao intranodal

  1. Intranodal Palisaded Myofibroblastoma: Radiological and Cytological Overview

    PubMed Central

    Altinbas, Namik Kemal; Oz, Ilker; Ustuner, Evren; Gulpinar, Basak; Peker, Elif; Akkaya, Zehra; Peker, Ahmet; Ceyhan, Koray; Yagci, Cemil

    2016-01-01

    Summary Background Intranodal palisaded myofibroblastoma is a benign and very rare mesenchymal neoplasm of the lymph nodes originating from differentiated smooth muscle cells and myofibroblasts. Case Report We report a case of intranodal palisaded myofibroblastoma in an 84-year-old woman with Parkinson’s disease that presented as a left inguinal mass. The diagnosis was made using ultrasound-guided fine needle aspiration biopsy and consequent cytopathological examination that included immunohistochemical analysis. Herein, we discuss the presentation of a rare intranodal palisaded myofibroblastoma with emphasis on its ultrasonographic and cytopathologic features. Conclusions Intranodal palisaded myofibroblastoma should be considered in the differential diagnosis of inguinal lymphadenopathy and the diagnosis is possible with cytopathologic exam and immunohistochemical analysis using ultrasound-guided FNA biopsy, guiding the clinician to nodal excision rather than aggressive measures. PMID:27504146

  2. Intranode data communications in a parallel computer

    DOEpatents

    Archer, Charles J; Blocksome, Michael A; Miller, Douglas R; Ratterman, Joseph D; Smith, Brian E

    2014-01-07

    Intranode data communications in a parallel computer that includes compute nodes configured to execute processes, where the data communications include: allocating, upon initialization of a first process of a computer node, a region of shared memory; establishing, by the first process, a predefined number of message buffers, each message buffer associated with a process to be initialized on the compute node; sending, to a second process on the same compute node, a data communications message without determining whether the second process has been initialized, including storing the data communications message in the message buffer of the second process; and upon initialization of the second process: retrieving, by the second process, a pointer to the second process's message buffer; and retrieving, by the second process from the second process's message buffer in dependence upon the pointer, the data communications message sent by the first process.

  3. Intranode data communications in a parallel computer

    DOEpatents

    Archer, Charles J; Blocksome, Michael A; Miller, Douglas R; Ratterman, Joseph D; Smith, Brian E

    2013-07-23

    Intranode data communications in a parallel computer that includes compute nodes configured to execute processes, where the data communications include: allocating, upon initialization of a first process of a compute node, a region of shared memory; establishing, by the first process, a predefined number of message buffers, each message buffer associated with a process to be initialized on the compute node; sending, to a second process on the same compute node, a data communications message without determining whether the second process has been initialized, including storing the data communications message in the message buffer of the second process; and upon initialization of the second process: retrieving, by the second process, a pointer to the second process's message buffer; and retrieving, by the second process from the second process's message buffer in dependence upon the pointer, the data communications message sent by the first process.

  4. Early diagnosis of lymph node metastasis: Importance of intranodal pressures.

    PubMed

    Miura, Yoshinobu; Mikada, Mamoru; Ouchi, Tomoki; Horie, Sachiko; Takeda, Kazu; Yamaki, Teppei; Sakamoto, Maya; Mori, Shiro; Kodama, Tetsuya

    2016-03-01

    Regional lymph node status is an important prognostic indicator of tumor aggressiveness. However, early diagnosis of metastasis using intranodal pressure, at a stage when lymph node size has not changed significantly, has not been investigated. Here, we use an MXH10/Mo-lpr/lpr mouse model of lymph node metastasis to show that intranodal pressure increases in both the subiliac lymph node and proper axillary lymph node, which are connected by lymphatic vessels, when tumor cells are injected into the subiliac lymph node to induce metastasis to the proper axillary lymph node. We found that intranodal pressure in the subiliac lymph node increased at the stage when metastasis was detected by in vivo bioluminescence, but when proper axillary lymph node volume (measured by high-frequency ultrasound imaging) had not increased significantly. Intravenously injected liposomes, encapsulating indocyanine green, were detected in solid tumors by in vivo bioluminescence, but not in the proper axillary lymph node. Basic blood vessel and lymphatic channel structures were maintained in the proper axillary lymph node, although sinus histiocytosis was detected. These results show that intranodal pressure in the proper axillary lymph node increases at early stages when metastatic tumor cells have not fully proliferated. Intranodal pressure may be a useful parameter for facilitating early diagnosis of lymph node metastasis. PMID:26716604

  5. Diagnostic Accuracy of Computer-Aided Assessment of Intranodal Vascularity in Distinguishing Different Causes of Cervical Lymphadenopathy.

    PubMed

    Ying, Michael; Cheng, Sammy C H; Ahuja, Anil T

    2016-08-01

    Ultrasound is useful in assessing cervical lymphadenopathy. Advancement of computer science technology allows accurate and reliable assessment of medical images. The aim of the study described here was to evaluate the diagnostic accuracy of computer-aided assessment of the intranodal vascularity index (VI) in differentiating the various common causes of cervical lymphadenopathy. Power Doppler sonograms of 347 patients (155 with metastasis, 23 with lymphoma, 44 with tuberculous lymphadenitis, 125 reactive) with palpable cervical lymph nodes were reviewed. Ultrasound images of cervical nodes were evaluated, and the intranodal VI was quantified using a customized computer program. The diagnostic accuracy of using the intranodal VI to distinguish different disease groups was evaluated and compared. Metastatic and lymphomatous lymph nodes tend to be more vascular than tuberculous and reactive lymph nodes. The intranodal VI had the highest diagnostic accuracy in distinguishing metastatic and tuberculous nodes with a sensitivity of 80%, specificity of 73%, positive predictive value of 91%, negative predictive value of 51% and overall accuracy of 68% when a cutoff VI of 22% was used. Computer-aided assessment provides an objective and quantitative way to evaluate intranodal vascularity. The intranodal VI is a useful parameter in distinguishing certain causes of cervical lymphadenopathy and is particularly useful in differentiating metastatic and tuberculous lymph nodes. However, it has limited value in distinguishing lymphomatous nodes from metastatic and reactive nodes. PMID:27131839

  6. Fibroblastic reticular cell-derived lysophosphatidic acid regulates confined intranodal T-cell motility

    PubMed Central

    Takeda, Akira; Kobayashi, Daichi; Aoi, Keita; Sasaki, Naoko; Sugiura, Yuki; Igarashi, Hidemitsu; Tohya, Kazuo; Inoue, Asuka; Hata, Erina; Akahoshi, Noriyuki; Hayasaka, Haruko; Kikuta, Junichi; Scandella, Elke; Ludewig, Burkhard; Ishii, Satoshi; Aoki, Junken; Suematsu, Makoto; Ishii, Masaru; Takeda, Kiyoshi; Jalkanen, Sirpa; Miyasaka, Masayuki; Umemoto, Eiji

    2016-01-01

    Lymph nodes (LNs) are highly confined environments with a cell-dense three-dimensional meshwork, in which lymphocyte migration is regulated by intracellular contractile proteins. However, the molecular cues directing intranodal cell migration remain poorly characterized. Here we demonstrate that lysophosphatidic acid (LPA) produced by LN fibroblastic reticular cells (FRCs) acts locally to LPA2 to induce T-cell motility. In vivo, either specific ablation of LPA-producing ectoenzyme autotaxin in FRCs or LPA2 deficiency in T cells markedly decreased intranodal T cell motility, and FRC-derived LPA critically affected the LPA2-dependent T-cell motility. In vitro, LPA activated the small GTPase RhoA in T cells and limited T-cell adhesion to the underlying substrate via LPA2. The LPA-LPA2 axis also enhanced T-cell migration through narrow pores in a three-dimensional environment, in a ROCK-myosin II-dependent manner. These results strongly suggest that FRC-derived LPA serves as a cell-extrinsic factor that optimizes T-cell movement through the densely packed LN reticular network. DOI: http://dx.doi.org/10.7554/eLife.10561.001 PMID:26830463

  7. In situ engineering of the lymph node microenvironment via intranodal injection of adjuvant-releasing polymer particles.

    PubMed

    Jewell, Christopher M; López, Sandra C Bustamante; Irvine, Darrell J

    2011-09-20

    Recent studies have demonstrated a simple, potentially universal strategy to enhance vaccine potency, via intralymph node (i.LN) injection. To date, intranodal immunization studies have focused on the delivery of unadjuvanted vaccines (e.g., naked DNA, peptide, or protein). We hypothesized that combining i.LN vaccination with controlled release biomaterials permitting sustained dosing of molecular adjuvants to the local tissue microenvironment would further enhance this promising vaccination strategy. To test this idea, we encapsulated the Toll-like receptor-3 ligand poly(inosinic:cytidylic acid) (polyIC) in biodegradable poly(lactide-co-glycolide) microparticles (MPs) designed to remain extracellular and release polyIC in the LN over several days. Intranodal injection of MPs increased persistence of polyIC in LNs compared to the same dose of soluble polyIC or polyIC formulated in nanoparticles, leading to increased accumulation of Toll-like receptor agonist in LN-resident antigen presenting cells and more enduring dendritic cell activation. Intralymph node injection of ovalbumin mixed with polyIC-releasing MPs enhanced the humoral response and expanded ovalbumin-specific T cells to frequencies as high as 18% among all CD8(+) cells following a single injection (8.2-fold greater than the same vaccine given i.m.), a response that could not be matched by antigen mixed with polyIC-loaded nanoparticles or a 10-fold greater dose of soluble polyIC. Thus, i.LN immunization with slow release-formulated adjuvants may be a broadly applicable strategy to enhance therapeutic or prophylactic vaccines. PMID:21896725

  8. Simulate-HEX - The multi-group diffusion equation in hexagonal-z geometry

    SciTech Connect

    Lindahl, S. O.

    2013-07-01

    The multigroup diffusion equation is solved for the hexagonal-z geometry by dividing each hexagon into 6 triangles. In each triangle, the Fourier solution of the wave equation is approximated by 8 plane waves to describe the intra-nodal flux accurately. In the end an efficient Finite Difference like equation is obtained. The coefficients of this equation depend on the flux solution itself and they are updated once per power/void iteration. A numerical example demonstrates the high accuracy of the method. (authors)

  9. INTRANODAL PALISADED MYOFIBROBLASTOMA: ANOTHER MESENCHYMAL NEOPLASM WITH CTNNB1 (BETA-CATENIN GENE) MUTATIONS. CLINICOPATHOLOGIC, IMMUNOHISTOCHEMICAL, AND MOLECULAR GENETIC STUDY OF 18 CASES

    PubMed Central

    Laskin, William B.; Lasota, Jerzy; Fetsch, John F.; Felisiak-Golabek, Anna; Wang, Zeng-Feng; Miettinen, Markku

    2014-01-01

    Intranodal palisaded myofibroblastoma is a benign, lymph node-based myofibroblastic tumor of unknown pathogenesis. We report the clinicopathological, immunohistochemical, and genetic molecular features of this rare entity. The study cohort consisted of 14 males and 4 females ranging in age from 31 to 65 (mean, 47; median 49) years with tumors arising in inguinal lymph nodes (n=15), a neck lymph node (n=1), and undesignated lymph nodes (n=2). Most individuals presented with a painless mass or lump. Possible trauma/injury to the inguinal region was documented in four cases. Tumors ranged in size from 1.0 to 4.2 (mean, 3.1; median; 3.0) cm. Microscopically, the process presented as a well-circumscribed, often times pseudoencapsulated nodule (n=17) or nodules (n=1). Tumors consisted of a cellular proliferation of cytologically bland, spindled cells arranged in short fascicles and whorls within a finely collagenous(n=11) or myxocollagenous(n=7) matrix. In 12 tumors, scattered fibromatosis-like fascicles of spindled cells were noted. Histological features characteristic of the process included nuclear palisades (n=16 cases), collagenous bodies (n=15), and perinuclear intracytoplasmic hyaline globules (n=10). Mitotic activity ranged from 0 to 8 (mean,2; median, 1) mitotic figures/50 high-powered fields with no atypical division figures identified. Immunohistochemically, all tumors tested expressed (vimentin (n=3), smooth-muscle actin and/or muscle-specific actin (n=5, each), and nuclear beta-catenin and cyclin D1 (n=8, each). The latter two results prompted a screening for mutations in the beta-catenin gene glycogen synthase kinase-3 beta phosphorylation mutational “hotspot” region in exon 3 using PCR amplification and Sanger sequencing. Single nucleotide substitutions leading to missense mutations at the protein level were identified in 7 of 8 (88%) analyzed tumors and are responsible for the abnormal expression of beta-catenin and cyclin D1. These results

  10. Risk factor analysis for massive lymphatic ascites after laparoscopic retroperitonal lymphadenectomy in gynecologic cancers and treatment using intranodal lymphangiography with glue embolization

    PubMed Central

    2016-01-01

    Objective To evaluate risk factors for massive lymphatic ascites after laparoscopic retroperitoneal lymphadenectomy in gynecologic cancer and the feasibility of treatments using intranodal lymphangiography (INLAG) with glue embolization. Methods A retrospective analysis of 234 patients with gynecologic cancer who received laparoscopic retroperitonal lymphadenectomy between April 2006 and November 2015 was done. In June 2014, INLAG with glue embolization was initiated to manage massive lymphatic ascites. All possible clinicopathologic factors related to massive lymphatic ascites were determined in the pre-INLAG group (n=163). Clinical courses between pre-INLAG group and post-INLAG group (n=71) were compared. Results In the pre-INLAG group (n=163), four patients (2.5%) developed massive lymphatic ascites postoperatively. Postoperative lymphatic ascites was associated with liver cirrhosis (three cirrhotic patients, p<0.001). In the post-INLAG group, one patient with massive lymphatic ascites had a congestive heart failure and first received INLAG with glue embolization. She had pelvic drain removed within 7 days after INLAG. The mean duration of pelvic drain and hospital stay decreased after the introduction of INLAG (13.2 days vs. 10.9 days, p=0.001; 15.2 days vs. 12.6 days, p=0.001). There was no evidence of recurrence after this procedure. Conclusion Underlying medical conditions related to the reduced effective circulating volume, such as liver cirrhosis and heart failure, may be associated with massive lymphatic ascites after retroperitoneal lymphadenectomy. INLAG with glue embolization can be an alternative treatment options to treat leaking lymphatic channels in patients with massive lymphatic leakage. PMID:27171674

  11. Molecular Geometry.

    ERIC Educational Resources Information Center

    Desseyn, H. O.; And Others

    1985-01-01

    Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…

  12. Dark Geometry

    NASA Astrophysics Data System (ADS)

    Cembranos, J. A. R.; Dobado, A.; Maroto, A. L.

    Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space-time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

  13. Geometry in Medias Res

    ERIC Educational Resources Information Center

    Cukier, Mimi; Asdourian, Tony; Thakker, Anand

    2012-01-01

    Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

  14. Dynamic Geometry on WWW.

    ERIC Educational Resources Information Center

    Kuntz, Gilles

    The first section of this paper on World Wide Web applications related to dynamic geometry addresses dynamic geometry and teaching, including the relationship between dynamic geometry and direct manipulation, key features of dynamic geometry environments, the importance of direct engagement of the learner using construction software for…

  15. Learning Geometry through Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Forsythe, Sue

    2007-01-01

    In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…

  16. Combinatorial Geometry Printer Plotting.

    Energy Science and Technology Software Center (ESTSC)

    1987-01-05

    Picture generates plots of two-dimensional slices through the three-dimensional geometry described by the combinatorial geometry (CG) package used in such codes as MORSE and QAD-CG. These plots are printed on a standard line printer.

  17. General 2 charge geometries

    NASA Astrophysics Data System (ADS)

    Taylor, Marika

    2006-03-01

    Two charge BPS horizon free supergravity geometries are important in proposals for understanding black hole microstates. In this paper we construct a new class of geometries in the NS1-P system, corresponding to solitonic strings carrying fermionic as well as bosonic condensates. Such geometries are required to account for the full microscopic entropy of the NS1-P system. We then briefly discuss the properties of the corresponding geometries in the dual D1-D5 system.

  18. Geometry and Erdkinder.

    ERIC Educational Resources Information Center

    McDonald, Nathaniel J.

    2001-01-01

    Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…

  19. The Beauty of Geometry

    ERIC Educational Resources Information Center

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  20. Geometry of multihadron production

    SciTech Connect

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

  1. Want to Play Geometry?

    ERIC Educational Resources Information Center

    Kaufmann, Matthew L.; Bomer, Megan A.; Powell, Nancy Norem

    2009-01-01

    Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…

  2. Euclidean Geometry via Programming.

    ERIC Educational Resources Information Center

    Filimonov, Rossen; Kreith, Kurt

    1992-01-01

    Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…

  3. Geometry + Technology = Proof

    ERIC Educational Resources Information Center

    Lyublinskaya, Irina; Funsch, Dan

    2012-01-01

    Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

  4. Gingerbread-House Geometry.

    ERIC Educational Resources Information Center

    Emenaker, Charles E.

    1999-01-01

    Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

  5. What Is Geometry?

    ERIC Educational Resources Information Center

    Chern, Shiing-Shen

    1990-01-01

    Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)

  6. Noncommutative Geometry and Physics

    NASA Astrophysics Data System (ADS)

    Connes, Alain

    2006-11-01

    In this very short essay we shall describe a "spectral" point of view on geometry which allows to start taking into account the lessons from both renormalization and of general relativity. We shall first do that for renormalization and explain in rough outline the content of our recent collaborations with Dirk Kreimer and Matilde Marcolli leading to the universal Galois symmetry of renormalizable quantum field theories provided by the renormalization group in its cosmic Galois group incarnation. As far as general relativity is concerned, since the functional integral cannot be treated in the traditional perturbative manner, it relies heavily as a "sum over geometries" on the chosen paradigm of geometric space. This will give us the occasion to discuss, in the light of noncommutative geometry, the issue of "observables" in gravity and our joint work with Ali Chamseddine on the spectral action, with a first attempt to write down a functional integral on the space of noncommutative geometries.

  7. Proof in Transformation Geometry

    ERIC Educational Resources Information Center

    Bell, A. W.

    1971-01-01

    The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

  8. Common Geometry Module

    Energy Science and Technology Software Center (ESTSC)

    2005-01-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and onmore » top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.« less

  9. CMS Geometry Through 2020

    NASA Astrophysics Data System (ADS)

    Osborne, I.; Brownson, E.; Eulisse, G.; Jones, C. D.; Lange, D. J.; Sexton-Kennedy, E.

    2014-06-01

    CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

  10. Geometry and Cloaking Devices

    NASA Astrophysics Data System (ADS)

    Ochiai, T.; Nacher, J. C.

    2011-09-01

    Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

  11. Students Discovering Spherical Geometry Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Guven, Bulent; Karatas, Ilhan

    2009-01-01

    Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

  12. The Helen of Geometry

    ERIC Educational Resources Information Center

    Martin, John

    2010-01-01

    The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.

  13. The Geometry of Viruses.

    ERIC Educational Resources Information Center

    Case, Christine L.

    1991-01-01

    Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)

  14. Gravity is Geometry.

    ERIC Educational Resources Information Center

    MacKeown, P. K.

    1984-01-01

    Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

  15. Sliding vane geometry turbines

    DOEpatents

    Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R

    2014-12-30

    Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.

  16. Making Solid Geometry Solid.

    ERIC Educational Resources Information Center

    Hartz, Viggo

    1981-01-01

    Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)

  17. Fractal geometry of music.

    PubMed Central

    Hsü, K J; Hsü, A J

    1990-01-01

    Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

  18. Geometry and physics

    PubMed Central

    Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

    2010-01-01

    We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

  19. GEOMETRY, TENTATIVE GUIDES.

    ERIC Educational Resources Information Center

    KLIER, KATHERINE M.

    PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…

  20. Geometry of spinor regularization

    NASA Technical Reports Server (NTRS)

    Hestenes, D.; Lounesto, P.

    1983-01-01

    The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.

  1. Listening to Geometry

    ERIC Educational Resources Information Center

    Cooper, Brett D.; Barger, Rita

    2009-01-01

    The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…

  2. Geometry of PDE's. IV

    NASA Astrophysics Data System (ADS)

    Prástaro, Agostino

    2008-02-01

    Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.

  3. An introduction to Minkowski geometries

    NASA Astrophysics Data System (ADS)

    Farnsworth, David L.

    2016-07-01

    The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.

  4. Physics and geometry

    NASA Astrophysics Data System (ADS)

    Souriau, Jean-Marie

    1983-01-01

    Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality. This holds at every level: The concept of “connexion,” for instance, is used in the construction of models of the universe as well as in the description of the interior of the proton. Nothing is apparently more contrary to the wisdom of physicists; all the same, “it works.” The pages that follow show the conceptual role played by this geometry in some examples—without entering into technical details. In order to achieve this, we shall often have to abandon the complete mathematical rigor and even full definitions; however, we shall be able to give a precise description of the connection of ideas thanks to some elements of group theory.

  5. Puzzle geometry and rigidity

    NASA Astrophysics Data System (ADS)

    Smania, Daniel

    2007-07-01

    We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps which admit a topological conjugacy, quasiconformal outside the filled-in Julia set, are indeed quasiconformally conjugate. The proof uses a new abstract removability-type result for quasiconformal maps, following ideas of Heinonen and Koskela and of Kallunki and Koskela, optimized for applications in complex dynamics. We prove, as the first application of this new method, that, for even criticalities distinct from two, the period two cycle of the Fibonacci renormalization operator is hyperbolic with 1 -dimensional unstable manifold.

  6. Failures of information geometry

    NASA Astrophysics Data System (ADS)

    Skilling, John

    2015-01-01

    Information H is a unique relationship between probabilities, based on the property of independence which is central to scientific methodology. Information Geometry makes the tempting but fallacious assumption that a local metric (conventionally based on information) can be used to endow the space of probability distributions with a preferred global Riemannian metric. No such global metric can conform to H, which is "from-to" asymmetric whereas geometrical length is by definition symmetric. Accordingly, any Riemannian metric will contradict the required structure of the very distributions which are supposedly being triangulated. It follows that probabilities do not form a metric space. We give counter-examples in which alternative formulations of information, and the use of information geometry, lead to unacceptable results.

  7. Cylindrical geometry hall thruster

    DOEpatents

    Raitses, Yevgeny; Fisch, Nathaniel J.

    2002-01-01

    An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.

  8. Freezing in confined geometries

    NASA Technical Reports Server (NTRS)

    Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.

    1992-01-01

    Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.

  9. Integral geometry and holography

    DOE PAGESBeta

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less

  10. Emergent Complex Network Geometry

    NASA Astrophysics Data System (ADS)

    Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra

    2015-05-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems.

  11. Emergent Complex Network Geometry

    PubMed Central

    Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra

    2015-01-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems. PMID:25985280

  12. Integral geometry and holography

    SciTech Connect

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

  13. Graded geometry and Poisson reduction

    SciTech Connect

    Cattaneo, A. S.; Zambon, M.

    2009-02-02

    The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.

  14. Geometry Career Unit: Junior High.

    ERIC Educational Resources Information Center

    Jensen, Daniel

    The guide, the product of an exemplary career education program for junior high school students, was developed to show how geometry can be applied to real-life career-oriented areas and to bring a practical approach to the teaching of geometry. It is designed to show how some of the theorems or postulates in geometry are used in different careers.…

  15. Geometry: Grades 10-12.

    ERIC Educational Resources Information Center

    Instructional Objectives Exchange, Los Angeles, CA.

    Behavioral objectives, each accompanied by six sample test items, for secondary school geometry are presented. Objectives were determined by surveying the most widely used secondary school geometry textbooks, and cover 14 major categories of geometry, with sections on set theory and introductory trigonometry. Answers are provided. Categories…

  16. Computer-Aided Geometry Modeling

    NASA Technical Reports Server (NTRS)

    Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)

    1984-01-01

    Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.

  17. Geometry of Quantum States

    NASA Astrophysics Data System (ADS)

    Bengtsson, Ingemar; Zyczkowski, Karol

    2006-05-01

    Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists

  18. Optically defined mechanical geometry

    NASA Astrophysics Data System (ADS)

    Barasheed, Abeer Z.; Müller, Tina; Sankey, Jack C.

    2016-05-01

    In the field of optomechanics, radiation forces have provided a particularly high level of control over the frequency and dissipation of mechanical elements. Here we propose a class of optomechanical systems in which light exerts a similarly profound influence over two other fundamental parameters: geometry and mass. By applying an optical trap to one lattice site of an extended phononic crystal, we show it is possible to create a tunable, localized mechanical mode. Owing to light's simultaneous and constructive coupling with the structure's continuum of modes, we estimate that a trap power at the level of a single intracavity photon should be capable of producing a significant effect within a realistic, chip-scale device.

  19. Critique of information geometry

    SciTech Connect

    Skilling, John

    2014-12-05

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  20. Geometry from Gauge Theory

    NASA Astrophysics Data System (ADS)

    Correa, Diego H.; Silva, Guillermo A.

    2008-07-01

    We discuss how geometrical and topological aspects of certain 1/2-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

  1. Geometry from Gauge Theory

    SciTech Connect

    Correa, Diego H.; Silva, Guillermo A.

    2008-07-28

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

  2. Critique of information geometry

    NASA Astrophysics Data System (ADS)

    Skilling, John

    2014-12-01

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  3. Planetary Image Geometry Library

    NASA Technical Reports Server (NTRS)

    Deen, Robert C.; Pariser, Oleg

    2010-01-01

    The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

  4. Information geometry of Bayesian statistics

    NASA Astrophysics Data System (ADS)

    Matsuzoe, Hiroshi

    2015-01-01

    A survey of geometry of Bayesian statistics is given. From the viewpoint of differential geometry, a prior distribution in Bayesian statistics is regarded as a volume element on a statistical model. In this paper, properties of Bayesian estimators are studied by applying equiaffine structures of statistical manifolds. In addition, geometry of anomalous statistics is also studied. Deformed expectations and deformed independeces are important in anomalous statistics. After summarizing geometry of such deformed structues, a generalization of maximum likelihood method is given. A suitable weight on a parameter space is important in Bayesian statistics, whereas a suitable weight on a sample space is important in anomalous statistics.

  5. GPS: Geometry, Probability, and Statistics

    ERIC Educational Resources Information Center

    Field, Mike

    2012-01-01

    It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

  6. Achievement in Writing Geometry Proofs.

    ERIC Educational Resources Information Center

    Senk, Sharon L.

    In 1981 a nationwide assessment of achievement in writing geometry proofs was conducted by the Cognitive Development and Achievement in Secondary School Geometry project. Over 1,500 students in 11 schools in 5 states participated. This paper describes the sample, instruments, grading procedures, and selected results. Results include: (1) at the…

  7. Limits of downstream hydraulic geometry

    NASA Astrophysics Data System (ADS)

    Wohl, Ellen

    2004-10-01

    Adjustments to flow width, depth, and velocity in response to changes in discharge are commonly characterized by using downstream hydraulic geometry relationships. The spatial limits of these relationships within a drainage basin have not been systematically quantified. Where the erosional resistance of the channel substrate is sufficiently large, hydraulic driving forces presumably will be unable to adjust channel form. Data sets from 10 mountain rivers in the United States, Panama, Nepal, and New Zealand are used in this study to explore the limits of downstream hydraulic geometry relationships. Where the ratio of stream power to sediment size (Ω/D84) exceeds 10,000 kg/s3, downstream hydraulic geometry is well developed; where the ratio falls below 10,000 kg/s3, downstream hydraulic geometry relationships are poorly developed. These limitations on downstream hydraulic geometry have important implications for channel engineering and simulations of landscape change.

  8. Lobachevsky's Geometry and Research of Geometry of the Universe

    NASA Astrophysics Data System (ADS)

    Brylevskaya, L. I.

    2008-10-01

    For the first time N. I. Lobachevsky gave a talk on the new geometry in 1826; three years after he had published a work "On the fundamentals of geometry", containing all fundamental theorems and methods of non-Euclidean geometry. A small part of the article was devoted to the study of geometry of the Universe. The interpretation of geometrical concepts in pure empirical way was typical for mathematicians at the beginning of the XIX century; in this connection it was important for scientists to find application of his geometry. Having the purpose to determine experimentally the properties of real physical Space, Lobachevsky decided to calculate the sum of angles in a huge triangle with two vertexes in opposite points of the terrestrial orbit and the third -- on the remote star. Investigating the possibilities of solution of the set task, Lobachevsky faced the difficulties of theoretical, technical and methodological character. More detailed research of different aspects of the problem led Lobachevsky to the comprehension of impossibility to obtain the values required for the goal achievement, and he called his geometry an imaginary geometry.

  9. Quantum Consequences of Parameterizing Geometry

    NASA Astrophysics Data System (ADS)

    Wanas, M. I.

    2002-12-01

    The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.

  10. Distance geometry and geometric algebra

    NASA Astrophysics Data System (ADS)

    Dress, Andreas W. M.; Havel, Timothy F.

    1993-10-01

    As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

  11. The Dilemma of Descriptive Geometry

    ERIC Educational Resources Information Center

    Boleslavski, Moshe

    1977-01-01

    Proposes that engineering students undergo a preparatory summer school training program in fundamentals of engineering drawing, descriptive geometry, and mathematics prior to being admitted to regular engineering studies. (SL)

  12. Emergent geometry from quantized spacetime

    SciTech Connect

    Yang, Hyun Seok; Sivakumar, M.

    2010-08-15

    We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.

  13. Interaction of morphogens with geometry

    NASA Astrophysics Data System (ADS)

    Cummings, F. W.

    2005-09-01

    Morphogen patterns are viewed as being affected by epithelial sheet geometry in early development. As the total area of the (closed) sheet changes, the changing geometry acts back in turn to change the morphogen pattern. A number of constraints are given on the functional form of the Gauss and Mean curvatures, considered as functions of the morphogen concentrations and their derivatives. It is shown that the constraints are sufficient to motivate a convincing dependence of the two curvatures on the morphogen concentrations.

  14. The Common Geometry Module (CGM).

    SciTech Connect

    Tautges, Timothy James

    2004-12-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

  15. Earthquake cycles in complex geometries

    NASA Astrophysics Data System (ADS)

    Romanet, Pierre; Bhat, Harsha; Madariaga, Raul

    2016-04-01

    Our understanding of earthquake cycles, from a modelling perspective, comes mainly from theoretical, and numerical, work on a single straight fault. However, natural fault systems are geometrically complex. Modelling complex fault geometry (bends, kinks and multiple faults) is in itself a challenge as it is computationally intensive. To overcome this difficulty, we appeal to the Fast Multipole Method which was developed in the context of modelling N-body problems. This method is then used to model the quasi-dynamic response of multiple faults, with complex geometries, that are governed by rate and state friction laws. Our preliminary findings tell us that when stress interaction between faults, due to complex geometry, is accounted then even strongly rate-weakening faults (a-b)<0 show a complex spectrum of slow slip and dynamic ruptures.

  16. Quantum geometry and gravitational entropy

    SciTech Connect

    Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan

    2007-05-29

    Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

  17. Hexatic undulations in curved geometries.

    PubMed

    Lenz, Peter; Nelson, David R

    2003-03-01

    We discuss the influence of two-dimensional hexatic order on capillary waves and undulation modes in spherical and cylindrical geometries. In planar geometries, extended bond-orientational order has only a minor effect on the fluctuations of liquid surfaces or lipid bilayers. However, in curved geometries, the long-wavelength spectrum of these ripples is altered. We calculate this frequency shift and discuss applications to spherical vesicles, liquid metal droplets, bubbles and cylindrical jets coated with surface-active molecules, and to multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability of charged droplets and bubbles, and for the Plateau-Rayleigh instability of liquid jets. PMID:12689068

  18. Conventionalism and integrable Weyl geometry

    NASA Astrophysics Data System (ADS)

    Pucheu, M. L.

    2015-03-01

    Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.

  19. Individualized Geometry: A Geometry Unit for the Intermediate Grades.

    ERIC Educational Resources Information Center

    Geissler, Dennis; Larson, Richard

    This geometry unit for the intermediate grades is based on the Holt Mathematics Series (levels 3-6), using the concepts of Individually Guided Education (IGE). It is divided into seven levels, one for grade 3 and two each for grades 4-6. Each is designed for both individual and group learning. A vocabulary list is used as a key for activities; a…

  20. Geometry of generalized depolarizing channels

    SciTech Connect

    Burrell, Christian K.

    2009-10-15

    A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.

  1. Geometry, topology, and string theory

    SciTech Connect

    Varadarajan, Uday

    2003-07-10

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  2. LOGO Based Instruction in Geometry.

    ERIC Educational Resources Information Center

    Yusuf, Mian Muhammad

    The objective of this pretest-posttest Quasi-Experimental Design study was to determine the effects of LOGO Based Instruction (LBI) compared to instruction by teacher lecture and pencil-and-paper activities on: (1) students' understanding of the concepts of point, ray, line, and line segment; (2) students' attitudes toward learning geometry,…

  3. Exploring Bundling Theory with Geometry

    ERIC Educational Resources Information Center

    Eckalbar, John C.

    2006-01-01

    The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…

  4. Computer Environments for Learning Geometry.

    ERIC Educational Resources Information Center

    Clements, Douglas H.; Battista, Michael T.

    1994-01-01

    Reviews research describing computer functions of construction-oriented computer environments and evaluates their contributions to students' learning of geometry. Topics discussed include constructing geometric concepts; the use of LOGO in elementary school mathematics; software that focuses on geometric construction; and implications for the…

  5. Dislocation dynamics in confined geometry

    NASA Astrophysics Data System (ADS)

    Gómez-García, D.; Devincre, B.; Kubin, L.

    1999-05-01

    A simulation of dislocation dynamics has been used to calculate the critical stress for a threading dislocation moving in a confined geometry. The optimum conditions for conducting simulations in systems of various sizes, down to the nanometer range, are defined. The results are critically compared with the available theoretical and numerical estimates for the problem of dislocation motion in capped layers.

  6. Improving Student Reasoning in Geometry

    ERIC Educational Resources Information Center

    Wong, Bobson; Bukalov, Larisa

    2013-01-01

    In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…

  7. Foucault pendulum through basic geometry

    NASA Astrophysics Data System (ADS)

    von Bergmann, Jens; von Bergmann, HsingChi

    2007-10-01

    We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.

  8. A Microcomputer Descriptive Geometry Tutorial.

    ERIC Educational Resources Information Center

    Zongyi, Zuo

    1990-01-01

    A software package which can aid descriptive geometry instruction is described. Included are the features of the software and the software configuration. This software has been honored as the best and most advanced software of its kind in the People's Republic of China. (KR)

  9. Exploring Fractal Geometry with Children.

    ERIC Educational Resources Information Center

    Vacc, Nancy Nesbitt

    1999-01-01

    Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…

  10. Logo Activities in Elementary Geometry.

    ERIC Educational Resources Information Center

    Libeskind, Shlomo; And Others

    These activities were designed for use at the University of Montana, where they were tested for four quarters in a mathematics for elementary teachers course on informal geometry. They are for use with Apple II-Plus computers with 64K memory or Apple IIe computers and MIT Logo. (Modifications are necessary if the activities are to be used with…

  11. Towards a Navajo Indian Geometry.

    ERIC Educational Resources Information Center

    Pinxten, Rik; And Others

    This book examines the Navajo system of spatial knowledge and describes a culture-based curriculum for the development of an intuitive geometry based on the child's experience of the physical world. Aspects of the Navajo cosmology relevant to spatial knowledge are discussed: the structure of the world; the dynamic nature of the universe;…

  12. Analogical Reasoning in Geometry Education

    ERIC Educational Resources Information Center

    Magdas, Ioana

    2015-01-01

    The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

  13. Spectral geometry of symplectic spinors

    NASA Astrophysics Data System (ADS)

    Vassilevich, Dmitri

    2015-10-01

    Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by Habermann, K. ["The Dirac operator on symplectic spinors," Ann. Global Anal. Geom. 13, 155-168 (1995)]. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.

  14. Teaching Geometry According to Euclid.

    ERIC Educational Resources Information Center

    Hartshorne, Robin

    2000-01-01

    This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…

  15. Noncommutative geometry inspired entropic inflation

    NASA Astrophysics Data System (ADS)

    Nozari, Kourosh; Akhshabi, Siamak

    2011-06-01

    Recently Verlinde proposed that gravity can be described as an emergent phenomena arising from changes in the information associated with the positions of material bodies. By using noncommutative geometry as a way to describe the microscopic microstructure of quantum spacetime, we derive modified Friedmann equation in this setup and study the entropic force modifications to the inflationary dynamics of early universe.

  16. Van Hiele Guidelines for Geometry.

    ERIC Educational Resources Information Center

    Davey, Geoff; Holliday, Jack

    1992-01-01

    Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

  17. General Relativity: Geometry Meets Physics

    ERIC Educational Resources Information Center

    Thomsen, Dietrick E.

    1975-01-01

    Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

  18. The basics of information geometry

    NASA Astrophysics Data System (ADS)

    Caticha, Ariel

    2015-01-01

    To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".

  19. The Idea of Order at Geometry Class.

    ERIC Educational Resources Information Center

    Rishel, Thomas

    The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

  20. Teaching Activity-Based Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba

    2013-01-01

    This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…

  1. Geometry in Transition: A Model of Emergent Geometry

    SciTech Connect

    Delgadillo-Blando, Rodrigo; O'Connor, Denjoe; Ydri, Badis

    2008-05-23

    We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent {alpha}=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.

  2. Geometry-invariant resonant cavities

    NASA Astrophysics Data System (ADS)

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-03-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

  3. Geometry-invariant resonant cavities

    PubMed Central

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-01-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103

  4. Geometry of area without length

    NASA Astrophysics Data System (ADS)

    Ho, Pei-Ming; Inami, Takeo

    2016-01-01

    To define a free string by the Nambu-Goto action, all we need is the notion of area, and mathematically the area can be defined directly in the absence of a metric. Motivated by the possibility that string theory admits backgrounds where the notion of length is not well defined but a definition of area is given, we study space-time geometries based on the generalization of a metric to an area metric. In analogy with Riemannian geometry, we define the analogues of connections, curvatures, and Einstein tensor. We propose a formulation generalizing Einstein's theory that will be useful if at a certain stage or a certain scale the metric is ill defined and the space-time is better characterized by the notion of area. Static spherical solutions are found for the generalized Einstein equation in vacuum, including the Schwarzschild solution as a special case.

  5. Information geometry of Boltzmann machines.

    PubMed

    Amari, S; Kurata, K; Nagaoka, H

    1992-01-01

    A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold. It is important to study the geometry of the neural manifold, rather than the behavior of a single network, in order to know the capabilities and limitations of neural networks of a fixed topology. Using the new theory of information geometry, a natural invariant Riemannian metric and a dual pair of affine connections on the Boltzmann neural network manifold are established. The meaning of geometrical structures is elucidated from the stochastic and the statistical point of view. This leads to a natural modification of the Boltzmann machine learning rule. PMID:18276427

  6. Extending dark optical trapping geometries.

    PubMed

    Arnold, Aidan S

    2012-07-01

    New counterpropagating geometries are presented for localizing ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an "optical revolver," axial lattices of rings, and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts. PMID:22743436

  7. Geometry Dependence of Stellarator Turbulence

    SciTech Connect

    H.E. Mynick, P. Xanthopoulos and A.H. Boozer

    2009-08-10

    Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.

  8. Orbit propagation in Minkowskian geometry

    NASA Astrophysics Data System (ADS)

    Roa, Javier; Peláez, Jesús

    2015-09-01

    The geometry of hyperbolic orbits suggests that Minkowskian geometry, and not Euclidean, may provide the most adequate description of the motion. This idea is explored in order to derive a new regularized formulation for propagating arbitrarily perturbed hyperbolic orbits. The mathematical foundations underlying Minkowski space-time are exploited to describe hyperbolic orbits. Hypercomplex numbers are introduced to define the rotations, vectors, and metrics in the problem: the evolution of the eccentricity vector is described on the Minkowski plane in terms of hyperbolic numbers, and the orbital plane is described on the inertial reference using quaternions. A set of eight orbital elements is introduced, namely a time-element, the components of the eccentricity vector in , the semimajor axis, and the components of the quaternion defining the orbital plane. The resulting formulation provides a deep insight into the geometry of hyperbolic orbits. The performance of the formulation in long-term propagations is studied. The orbits of four hyperbolic comets are integrated and the accuracy of the solution is compared to other regularized formulations. The resulting formulation improves the stability of the integration process and it is not affected by the perihelion passage. It provides a level of accuracy that may not be reached by the compared formulations, at the cost of increasing the computational time.

  9. Network geometry with flavor: From complexity to quantum geometry

    NASA Astrophysics Data System (ADS)

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

  10. Network geometry with flavor: From complexity to quantum geometry.

    PubMed

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its

  11. The Effect of Geometry Instruction with Dynamic Geometry Software; GeoGebra on Van Hiele Geometry Understanding Levels of Students

    ERIC Educational Resources Information Center

    Kutluca, Tamer

    2013-01-01

    The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…

  12. Optimizing solar-cell grid geometry

    NASA Technical Reports Server (NTRS)

    Crossley, A. P.

    1969-01-01

    Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.

  13. A Whirlwind Tour of Computational Geometry.

    ERIC Educational Resources Information Center

    Graham, Ron; Yao, Frances

    1990-01-01

    Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

  14. The Geometry of Quasar Outflows

    NASA Astrophysics Data System (ADS)

    Ganguly, Rajib

    2012-10-01

    Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.

  15. Rotating convection in elliptical geometries

    NASA Astrophysics Data System (ADS)

    Evonuk, M.

    2014-12-01

    Tidal interactions between hot jupiter planets and their host stars are likely to result in non-spherical geometries. These elliptical instabilities may have interesting effects on interior fluid convective patterns, which in turn influence the nature of the magnetic dynamo within these planets. Simulations of thermal convection in the 2D rotating equatorial plane are conducted to determine to first order the effect of ellipticity on convection for varying density contrasts with differing convective vigor and rotation rate. This survey is conducted in two dimensions in order to simulate a broad range of ellipticities and to maximize the parameter space explored.

  16. Worldsheet geometries of ambitwistor string

    NASA Astrophysics Data System (ADS)

    Ohmori, Kantaro

    2015-06-01

    Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.

  17. Emergent Calabi-Yau geometry.

    PubMed

    Ooguri, Hirosi; Yamazaki, Masahito

    2009-04-24

    We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold. PMID:19518695

  18. Engaging All Students with "Impossible Geometry"

    ERIC Educational Resources Information Center

    Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.

    2010-01-01

    Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…

  19. Geometry: Career Related Units. Teacher's Edition.

    ERIC Educational Resources Information Center

    Pierro, Mike; And Others

    Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…

  20. Preservice Primary School Teachers' Elementary Geometry Knowledge

    ERIC Educational Resources Information Center

    Marchis, Iuliana

    2012-01-01

    Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…

  1. Teaching Geometry: An Experiential and Artistic Approach.

    ERIC Educational Resources Information Center

    Ogletree, Earl J.

    The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…

  2. Fisher information geometry of the barycenter map

    NASA Astrophysics Data System (ADS)

    Itoh, Mitsuhiro; Satoh, Hiroyasu

    2015-01-01

    We report Fisher information geometry of the barycenter map associated with Busemann function Bθ of an Hadamard manifold X and present its application to Riemannian geometry of X from viewpoint of Fisher information geometry. This report is an improvement of [I-Sat'13] together with a fine investigation of the barycenter map.

  3. Geometry in the Early Years: A Commentary

    ERIC Educational Resources Information Center

    Dindyal, Jaguthsing

    2015-01-01

    The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

  4. Neuronal activity controls transsynaptic geometry.

    PubMed

    Glebov, Oleg O; Cox, Susan; Humphreys, Lawrence; Burrone, Juan

    2016-01-01

    The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792

  5. Quanta of Geometry: Noncommutative Aspects

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

  6. Weyl gravity and Cartan geometry

    NASA Astrophysics Data System (ADS)

    Attard, J.; François, J.; Lazzarini, S.

    2016-04-01

    We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].

  7. Turbine engine variable geometry device

    NASA Technical Reports Server (NTRS)

    Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)

    1985-01-01

    A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.

  8. Target Detection Using Fractal Geometry

    NASA Technical Reports Server (NTRS)

    Fuller, J. Joseph

    1991-01-01

    The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.

  9. Neuronal activity controls transsynaptic geometry

    PubMed Central

    Glebov, Oleg O.; Cox, Susan; Humphreys, Lawrence; Burrone, Juan

    2016-01-01

    The neuronal synapse is comprised of several distinct zones, including presynaptic vesicle zone (SVZ), active zone (AZ) and postsynaptic density (PSD). While correct relative positioning of these zones is believed to be essential for synaptic function, the mechanisms controlling their mutual localization remain unexplored. Here, we employ high-throughput quantitative confocal imaging, super-resolution and electron microscopy to visualize organization of synaptic subdomains in hippocampal neurons. Silencing of neuronal activity leads to reversible reorganization of the synaptic geometry, resulting in a increased overlap between immunostained AZ and PSD markers; in contrast, the SVZ-AZ spatial coupling is decreased. Bayesian blinking and bleaching (3B) reconstruction reveals that the distance between the AZ-PSD distance is decreased by 30 nm, while electron microscopy shows that the width of the synaptic cleft is decreased by 1.1 nm. Our findings show that multiple aspects of synaptic geometry are dynamically controlled by neuronal activity and suggest mutual repositioning of synaptic components as a potential novel mechanism contributing to the homeostatic forms of synaptic plasticity. PMID:26951792

  10. Quanta of geometry: noncommutative aspects.

    PubMed

    Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes. PMID:25793795

  11. Geometry and the quantum: basics

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav

    2014-12-01

    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.

  12. Alternative cosmology from cusp geometries

    NASA Astrophysics Data System (ADS)

    Rosa, Reinaldo; Herbin Stalder Díaz, Diego

    We study an alternative geometrical approach on the problem of classical cosmological singularity. It is based on a generalized function f(x,y)=x(2+y^2=(1-z)z^n) which consists of a cusped projected coupled isosurface. Such a projected geometry is computed and analized into the context of Friedmann singularity-free cosmology where a pre-big bang scenario is considered. Assuming that the mechanism of cusp formation is described by non-linear oscillations of a pre- big bang extended very high energy density field (>3x10^{94} kg/m^3$), we show that the action under the gravitational field follows a tautochrone of revolution, understood here as the primary projected geometry that alternatively replaces the Friedmann singularity in the standard big bang theory. As shown here this new approach allows us to interpret the nature of both matter and dark energy from first geometric principles [1]. [1] Rosa et al. DOI: 10.1063/1.4756991

  13. Differential Geometry Based Multiscale Models

    PubMed Central

    Wei, Guo-Wei

    2010-01-01

    Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that

  14. Clustering Implies Geometry in Networks

    NASA Astrophysics Data System (ADS)

    Krioukov, Dmitri

    2016-05-01

    Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity.

  15. Spinors in Physics and Geometry

    NASA Astrophysics Data System (ADS)

    Trautman, A.; Furlan, G.

    1988-11-01

    The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants

  16. Chemical shift driven geometry optimization.

    PubMed

    Witter, Raiker; Priess, Wolfram; Sternberg, Ulrich

    2002-01-30

    A new method for refinement of 3D molecular structures by geometry optimization is presented. Prerequisites are a force field and a very fast procedure for the calculation of chemical shifts in every step of optimization. To the energy, provided by the force field (COSMOS force field), a pseudoenergy, depending on the difference between experimental and calculated chemical shifts, is added. In addition to the energy gradients, pseudoforces are computed. This requires the derivatives of the chemical shifts with respect to the coordinates. The pseudoforces are analytically derived from the integral expressions of the bond polarization theory. Single chemical shift values attributed to corresponding atoms are considered for structural correction. As a first example, this method is applied for proton position refinement of the D-mannitol X-ray structure. A crystal structure refinement with 13C chemical shift pseudoforces is carried out. PMID:11924742

  17. Clustering Implies Geometry in Networks.

    PubMed

    Krioukov, Dmitri

    2016-05-20

    Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in an ensemble of random geometric graphs. Here we identify structural properties of networks that guarantee that random graphs having these properties are geometric. Specifically we show that random graphs in which expected degree and clustering of every node are fixed to some constants are equivalent to random geometric graphs on the real line, if clustering is sufficiently strong. Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity. The methods we use to prove this are quite general and applicable to other network ensembles, geometric or not, and to certain problems in quantum gravity. PMID:27258887

  18. Changing the Structure Boundary Geometry

    SciTech Connect

    Karasev, Viktor; Dzlieva, Elena; Ivanov, Artyom

    2008-09-07

    Analysis of previously obtained results shows that hexagonal crystal lattice is the dominant type of ordering, in particular, in striated glow discharges. We explore the possibility for changing the dust distribution in horizontal cross sections of relatively highly ordered structures in a glow-discharge. Presuming that boundary geometry can affect dust distribution, we used cylindrical coolers held at 0 deg. C and placed against a striation containing a structure, to change the geometry of its outer boundary. By varying the number of coolers, their positions, and their separations from the tube wall, azimuthally asymmetric thermophoretic forces can be used to form polygonal boundaries and vary the angles between their segments (in a horizontal cross section). The corner in the structure's boundary of 60 deg. stimulates formation of hexagonal cells. The structure between the supported parallel boundaries is also characterized by stable hexagonal ordering. We found that a single linear boundary segment does not give rise to any sizable domain, but generates a lattice extending from the boundary (without edge defects). A square lattice can be formed by setting the angle equal to 90 deg. . However, angles of 45 deg. and 135 deg. turned out easier to form. Square lattice was created by forming a near-135 deg. corner with four coolers. It was noted that no grain ordering is observed in the region adjacent to corners of angles smaller than 30 deg. , which do not promote ordering into cells of any shape. Thus, manipulation of a structure boundary can be used to change dust distribution, create structures free of the ubiquitous edge defects that destroy orientation order, and probably change the crystal lattice type.

  19. Geometry of discrete quantum computing

    NASA Astrophysics Data System (ADS)

    Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung

    2013-05-01

    Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.

  20. Convection in Slab and Spheroidal Geometries

    NASA Technical Reports Server (NTRS)

    Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

    2000-01-01

    Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

  1. Geometry of solar coronal rays

    NASA Astrophysics Data System (ADS)

    Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.

    2016-02-01

    Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field

  2. Riemannian geometry of fluctuation theory: An introduction

    NASA Astrophysics Data System (ADS)

    Velazquez, Luisberis

    2016-05-01

    Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.

  3. Use of CAD Geometry in MDO

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    1996-01-01

    The purpose of this paper is to discuss the use of Computer-Aided Design (CAD) geometry in a Multi-Disciplinary Design Optimization (MDO) environment. Two techniques are presented to facilitate the use of CAD geometry by different disciplines, such as Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM). One method is to transfer the load from a CFD grid to a CSM grid. The second method is to update the CAD geometry for CSM deflection.

  4. Geometry Software Common to All Experiments

    NASA Technical Reports Server (NTRS)

    1984-01-01

    All imaging, remote sensing, and in situ experiments require information about the geometry and location of observations. An alterntive to collecting geometry data with a supplementary experiment data record is proposed. The new method involves identifying the fundamental information, that is, the geometric state upon which geometry calculations are based, and maintaining or delivering these calculations in separate packages which are easily replaced when improved information is available. Implementation of this method in spacecraft navigation is discussed along with software system requirements.

  5. Geometry-induced asymmetric diffusion

    PubMed Central

    Shaw, Robert S.; Packard, Norman; Schröter, Matthias; Swinney, Harry L.

    2007-01-01

    Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels. PMID:17522257

  6. Linguistic geometry for technologies procurement

    NASA Astrophysics Data System (ADS)

    Stilman, Boris; Yakhnis, Vladimir; Umanskiy, Oleg; Boyd, Ron

    2005-05-01

    In the modern world of rapidly rising prices of new military hardware, the importance of Simulation Based Acquisition (SBA) is hard to overestimate. With SAB, DOD would be able to test, develop CONOPS for, debug, and evaluate new conceptual military equipment before actually building the expensive hardware. However, only recently powerful tools for real SBA have been developed. Linguistic Geometry (LG) permits full-scale modeling and evaluation of new military technologies, combinations of hardware systems and concepts of their application. Using LG tools, the analysts can create a gaming environment populated with the Blue forces armed with the new conceptual hardware as well as with appropriate existing weapons and equipment. This environment will also contain the intelligent enemy with appropriate weaponry and, if desired, with a conceptual counters to the new Blue weapons. Within such LG gaming environment, the analyst can run various what-ifs with the LG tools providing the simulated combatants with strategies and tactics solving their goals with minimal resources spent.

  7. Eye movements and information geometry.

    PubMed

    Lenz, Reiner

    2016-08-01

    The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database. PMID:27505658

  8. Cusp geometry in MHD simulations

    NASA Astrophysics Data System (ADS)

    Siscoe, George; Crooker, Nancy; Siebert, Keith; Maynard, Nelson; Weimer, Daniel; White, Willard

    2005-01-01

    The MHD simulations described here show that the latitude of the high-altitude cusp decreases as the IMF swings from North to South, that there is a pronounced dawn dusk asymmetry at high-altitude associated with a dawn dusk component of the IMF, and that at the same time there is also a pronounced dawn dusk asymmetry at low-altitude. The simulations generate a feature that represents what has been called the cleft. It appears as a tail (when the IMF has a By component) attached to the cusp, extending either toward the dawn flank or the dusk flank depending on the dawn dusk orientation of the IMF. This one-sided cleft connects the cusp to the magnetospheric sash. We compare cusp geometry predicted by MHD simulations against published observations based on Hawkeye and DMSP data. Regarding the high-altitude predictions, the comparisons are not definitive, mainly because the observations are incomplete or mutually inconsistent. Regarding the low-altitude prediction of a strong dawn dusk asymmetry, the observations are unambiguous and are in good qualitative agreement with the prediction.

  9. PREFACE: Water in confined geometries

    NASA Astrophysics Data System (ADS)

    Rovere, Mauro

    2004-11-01

    The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is

  10. Detonation diffraction through different geometries

    NASA Astrophysics Data System (ADS)

    Sorin, Rémy; Zitoun, Ratiba; Khasainov, Boris; Desbordes, Daniel

    2009-04-01

    We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d c = k c · λ (with λ the detonation cell size and k c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter ( D/ d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/ λ. For ratios below k c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k lim (which depends on D/ d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k c by 50%. The results in configuration C show that the re-ignition process depends both on d/ λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D ch = 200 mm) at as small d/ λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.

  11. Quantum groups: Geometry and applications

    SciTech Connect

    Chu, C.S.

    1996-05-13

    The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.

  12. Stop Teaching and Let Students Learn Geometry

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Adu-Gyamfi, Kwaku

    2011-01-01

    For many high school students as well as preservice teachers, geometry can be difficult to learn without experiences that allow them to build their own understanding. The authors' approach to geometry instruction--with its integration of content, multiple representations, real-world examples, reading and writing, communication and collaboration as…

  13. Improving African American Achievement in Geometry Honors

    ERIC Educational Resources Information Center

    Mims, Adrian B.

    2010-01-01

    This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…

  14. Normal faults geometry and morphometry on Mars

    NASA Astrophysics Data System (ADS)

    Vaz, D. A.; Spagnuolo, M. G.; Silvestro, S.

    2014-04-01

    In this report, we show how normal faults scarps geometry and degradation history can be accessed using high resolution imagery and topography. We show how the initial geometry of the faults can be inferred from faulted craters and we demonstrate how a comparative morphometric analysis of faults scarps can be used to study erosion rates through time on Mars.

  15. Teaching Geometry to Visually Impaired Students

    ERIC Educational Resources Information Center

    Pritchard, Christine K.; Lamb, John H.

    2012-01-01

    NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

  16. Teaching Geometry through Problem-Based Learning

    ERIC Educational Resources Information Center

    Schettino, Carmel

    2011-01-01

    About seven years ago, the mathematics teachers at the author's secondary school came to the conclusion that they were not satisfied with their rather traditional geometry textbook. The author had already begun using a problem-based approach to teaching geometry in her classes, a transition for her and her students that inspired her to write about…

  17. Quilt Blocks: Writing in the Geometry Classroom

    ERIC Educational Resources Information Center

    Gibson, Michelle; Thomas, Timothy G.

    2005-01-01

    The introduction of quilt pattern consisting of many quilt blocks formed by congruent triangles, for writing by the students in the geometry classrooms, is studied. It is found that the students enjoyed this method and writing also helped in understanding the geometric concepts expanding their vocabulary in geometry.

  18. A Multivariate Model of Achievement in Geometry

    ERIC Educational Resources Information Center

    Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha

    2014-01-01

    Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

  19. An approach for management of geometry data

    NASA Technical Reports Server (NTRS)

    Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

    1980-01-01

    The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

  20. Geometry, Student's Text, Part II, Unit 14.

    ERIC Educational Resources Information Center

    Allen, Frank B.; And Others

    Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…

  1. Teaching Molecular Geometry with the VSEPR Model

    ERIC Educational Resources Information Center

    Gillespie, Ronald J.

    2004-01-01

    The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…

  2. Historical Digressions in Greek Geometry Lessons.

    ERIC Educational Resources Information Center

    Thomaidis, Yannis

    1991-01-01

    Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…

  3. The Microcomputer and Instruction in Geometry.

    ERIC Educational Resources Information Center

    Kantowski, Mary Grace

    1981-01-01

    The microcomputer has great potential for making high school geometry more stimulating and more easily understood by the students. The microcomputer can facilitate instruction in both the logico-deductive and spatial-visual aspects of geometry through graphics representations, simulation of motion, and its capability of interacting with the…

  4. Computing Bisectors in a Dynamic Geometry Environment

    ERIC Educational Resources Information Center

    Botana, Francisco

    2013-01-01

    In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…

  5. Increased Knowledge in Geometry and Instructional Practice.

    ERIC Educational Resources Information Center

    Swafford, Jane O.; And Others

    1997-01-01

    Examines the effects on instruction of an intervention program designed to enhance teachers' knowledge of geometry and their knowledge of research on student cognition in geometry. Findings indicate significant gains in content knowledge and in van Hiele level, and marked changes in what was taught, how it was taught, and the characteristics…

  6. Linking Theory and Practice in Teaching Geometry

    ERIC Educational Resources Information Center

    Groth, Randall E.

    2005-01-01

    Several examples proved Van Hiele theory to be a useful ingredient in teaching of a summer course for high school students who had failed geometry during the school year are discussed. The theory provided a framework to help organize and reflect upon instruction for some key concepts in geometry.

  7. Making Euclidean Geometry Compulsory: Are We Prepared?

    ERIC Educational Resources Information Center

    Van Putten, Sonja; Howie, Sarah; Stols, Gerrit

    2010-01-01

    This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…

  8. The slab geometry laser. I - Theory

    NASA Technical Reports Server (NTRS)

    Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.

    1984-01-01

    Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.

  9. Reasoning by Contradiction in Dynamic Geometry

    ERIC Educational Resources Information Center

    Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra

    2013-01-01

    This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…

  10. The Geometry of the Universe: Part 2

    ERIC Educational Resources Information Center

    Francis, Stephanie

    2009-01-01

    Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

  11. Four-Dimensional Geometry: An Introduction.

    ERIC Educational Resources Information Center

    Hess, Adrien L.

    This document presents six chapters on four-dimensional geometry, whose titles are: (1) A Brief History; (2) What Is Four-Dimensional Geometry?; (3) Selected Drawings and Models; (4) How to Study the Configurations; (5) Selected Topics; and (6) Applications. The text, suitable for students in advanced levels of secondary school mathematics,…

  12. FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

    SciTech Connect

    Singer, Isadore M.

    2008-03-04

    The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

  13. Inquiry-Based Instruction in Geometry: The Impact on End of Course Geometry Test Scores

    ERIC Educational Resources Information Center

    Lewis, Betty

    2009-01-01

    Research examining instruction in geometry and standardized tests suggests that students have difficulty grasping geometry concepts and developing problem solving skills. The purpose of this study was to examine the relationship between the use of inquiry-based strategies in a geometry class and achievement on the end of course test (EOCT) and to…

  14. A Vector Approach to Euclidean Geometry: Vector Spaces and Affine Geometry, Volume 1. Teacher's Edition.

    ERIC Educational Resources Information Center

    Vaughan, Herbert E.; Szabo, Steven

    This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

  15. Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

    ERIC Educational Resources Information Center

    Mammana, M. F.; Micale, B.; Pennisi, M.

    2012-01-01

    We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

  16. Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

    ERIC Educational Resources Information Center

    Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

    2012-01-01

    This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

  17. Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry

    ERIC Educational Resources Information Center

    Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare

    2013-01-01

    A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…

  18. Heuristic Approach to the Schwarzschild Geometry

    NASA Astrophysics Data System (ADS)

    Visser, Matt

    In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé-Gullstrand coordinates. This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner-Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space. Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.

  19. Stokes flow in ellipsoidal geometry

    NASA Astrophysics Data System (ADS)

    Vafeas, Panayiotis; Dassios, George

    2006-09-01

    Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich-Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading

  20. tt * geometry in 3 and 4 dimensions

    NASA Astrophysics Data System (ADS)

    Cecotti, Sergio; Gaiotto, Davide; Vafa, Cumrun

    2014-05-01

    We consider the vacuum geometry of supersymmetric theories with 4 supercharges, on a flat toroidal geometry. The 2 dimensional vacuum geometry is known to be captured by the tt * geometry. In the case of 3 dimensions, the parameter space is ( T 2 × ) N and the vacuum geometry turns out to be a solution to a generalization of monopole equations in 3 N dimensions where the relevant topological ring is that of line operators. We compute the generalization of the 2d cigar amplitudes, which lead to S 2 × S 1 or S 3 partition functions which are distinct from the supersymmetric partition functions on these spaces, but reduce to them in a certain limit. We show the sense in which these amplitudes generalize the structure of 3d Chern-Simons theories and 2d RCFT's. In the case of 4 dimensions the parameter space is of the form X M,N = ( T 3 × ) M × T 3 N , and the vacuum geometry is a solution to a mixture of generalized monopole equations and generalized instanton equations (known as hyper-holomorphic connections). In this case the topological rings are associated to surface operators. We discuss the physical meaning of the generalized Nahm transforms which act on all of these geometries.

  1. Detection of edges using local geometry

    NASA Technical Reports Server (NTRS)

    Gualtieri, J. A.; Manohar, M.

    1989-01-01

    Researchers described a new representation, the local geometry, for early visual processing which is motivated by results from biological vision. This representation is richer than is often used in image processing. It extracts more of the local structure available at each pixel in the image by using receptive fields that can be continuously rotated and that go to third order spatial variation. Early visual processing algorithms such as edge detectors and ridge detectors can be written in terms of various local geometries and are computationally tractable. For example, Canny's edge detector has been implemented in terms of a local geometry of order two, and a ridge detector in terms of a local geometry of order three. The edge detector in local geometry was applied to synthetic and real images and it was shown using simple interpolation schemes that sufficient information is available to locate edges with sub-pixel accuracy (to a resolution increase of at least a factor of five). This is reasonable even for noisy images because the local geometry fits a smooth surface - the Taylor series - to the discrete image data. Only local processing was used in the implementation so it can readily be implemented on parallel mesh machines such as the MPP. Researchers expect that other early visual algorithms, such as region growing, inflection point detection, and segmentation can also be implemented in terms of the local geometry and will provide sufficiently rich and robust representations for subsequent visual processing.

  2. Geometry of Thin Nematic Elastomer Sheets

    NASA Astrophysics Data System (ADS)

    Aharoni, Hillel; Sharon, Eran; Kupferman, Raz

    A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this talk we describe the intrinsic geometry of such a sheet, and derive an expression for the metric induced by general smooth nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry. We provide an explicit analytical recipe for constructing any surface of revolution using this method. We demonstrate how the design of an arbitrary 2D geometry is accessible using approximate numerical methods.

  3. Emergence of wave equations from quantum geometry

    NASA Astrophysics Data System (ADS)

    Majid, Shahn

    2012-10-01

    We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.

  4. Writing and Speaking to Learn Geometry.

    ERIC Educational Resources Information Center

    Myers, Nadine C.

    1991-01-01

    Describes an intermediate level, college geometry course that is designated as both writing and speaking intensive. Suggests methods that utilize writing and speaking activities to enhance student learning, and discusses student reactions to the course. (nine references) (JJK)

  5. The geometry of dual isomonodromic deformations

    NASA Astrophysics Data System (ADS)

    Sanguinetti, G.; Woodhouse, N. M. J.

    2004-09-01

    The JMMS equations are studied using the geometry of the spectral curve of a pair of dual systems. It is shown that the equations can be represented as time-independent Hamiltonian flows on a Jacobian bundle.

  6. Minimal five dimensional supergravities and complex geometries

    SciTech Connect

    Herdeiro, Carlos A. R.

    2010-07-28

    We discuss the relation between solutions admitting Killing spinors of minimal super-gravities in five dimensions, both timelike and null, and complex geometries. For the timelike solutions the results may be summarised as follows. In the ungauged case (vanishing cosmological constant {Lambda} 0) the solutions are determined in terms of a hyper-Kaehler base space; in the gauged case ({Lambda}<0) the complex geometry is Kaehler; in the de Sitter case ({Lambda}>0) the complex geometry is hyper-Kaehler with torsion (HKT). For the null solutions we shall focus on the de Sitter case, for which the solutions are determined by a constrained Einstein-Weyl 3-geometry called Gauduchon-Tod space. The method for constructing explicit solutions is discussed in each case.

  7. Narrow Vertical Caves: Mapping Volcanic Fissure Geometries

    NASA Astrophysics Data System (ADS)

    Parcheta, C.; Nash, J.; Parness, A.; Mitchell, K. L.; Pavlov, C. A.

    2015-10-01

    Volcanic conduits are difficult to quantify, but their geometry fundamentally influences how eruptions occur. We robotically map old fissure conduits - elongated narrow cracks in the ground that transported magma to the surface during an eruption.

  8. The Oak Leaf: Connecting Geometry and Biology.

    ERIC Educational Resources Information Center

    Snyder, Judy

    1999-01-01

    Presents an activity that integrates biology and mathematics. Involves students in actual biological research and uses geometry, statistics, and computers to interpret data about the leaves of a tree. (ASK)

  9. Emergence of wave equations from quantum geometry

    SciTech Connect

    Majid, Shahn

    2012-09-24

    We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.

  10. Fractal Geometry in the High School Classroom.

    ERIC Educational Resources Information Center

    Camp, Dane R.

    1995-01-01

    Discusses classroom activities that involve applications of fractal geometry. Includes an activity sheet that explores Pascal's triangle, Sierpinsky's gasket, and modular arithmetic in two and three dimensions. (Author/MKR)

  11. Robot Geometry and the High School Curriculum.

    ERIC Educational Resources Information Center

    Meyer, Walter

    1988-01-01

    Description of the field of robotics and its possible use in high school computational geometry classes emphasizes motion planning exercises and computer graphics displays. Eleven geometrical problems based on robotics are presented along with the correct solutions and explanations. (LRW)

  12. Computational field simulation of temporally deforming geometries

    SciTech Connect

    Boyalakuntla, K.; Soni, B.K.; Thornburg, H.J.

    1996-12-31

    A NURBS based moving grid generation technique is presented to simulate temporally deforming geometries. Grid generation for a complex configuration can be a time consuming process and temporally varying geometries necessitate the regeneration of such a grid for every time step. The Non Uniform Rational B Spline (NURBS) based control point information is used for geometry description. The parametric definition of the NURBS is utilized in the development of the methodology to generate well distributed grid in a timely manner. The numerical simulation involving temporally deforming geometry is accomplished by appropriately linking to a unsteady, multi-block, thin layer Navier-Stokes solver. The present method greatly reduces CPU requirements for time dependent remeshing, facilitating the simulation of more complex unsteady problems. This current effort is the first step towards multidisciplinary design optimization, which involves coupling aerodynamic heat transfer and structural analysis. Applications include simulation of temporally deforming bodies.

  13. Structure analysis for plane geometry figures

    NASA Astrophysics Data System (ADS)

    Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi

    2013-12-01

    As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.

  14. Phase distribution in complex geometry conduits

    SciTech Connect

    Lahey, R.T. Jr.; Lopez de Bertodano, M.; Jones, O.C. Jr.

    1992-12-31

    Some of the most important and challenging problems in two-phase flow today have to do with the understanding and prediction of multidimensional phenomena, in particular, lateral phase distribution in both simple and complex geometry conduits. A prior review paper summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paper is to update that review, with particular emphasis on complex geometry conduit predictive capabilities.

  15. Supersymmetric geometries of IIA supergravity II

    NASA Astrophysics Data System (ADS)

    Gran, Ulf; Papadopoulos, George; von Schultz, Christian

    2015-12-01

    We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor equations impose some mild constraints on the geometry of the spacetime which include the existence of a time-like Killing vector field which leaves the fields and the Killing spinor invariant.

  16. Twisted geometries, twistors, and conformal transformations

    NASA Astrophysics Data System (ADS)

    Lângvik, Miklos; Speziale, Simone

    2016-07-01

    The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a timelike direction singled out. The isomorphism depends on the Immirzi parameter γ and reduces to the identity for γ =∞ . Using this twistorial representation, we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a one-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one—that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view and compare it with a discretization of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit, its action has an interesting nonlinear structure but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [Classical Quantum Gravity 32, 195015 (2015)].

  17. Geometry-induced protein pattern formation

    PubMed Central

    Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin

    2016-01-01

    Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in Δ EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems. PMID:26739566

  18. Holomorphic Parabolic Geometries and Calabi-Yau Manifolds

    NASA Astrophysics Data System (ADS)

    McKay, Benjamin

    2011-09-01

    We prove that the only complex parabolic geometries on Calabi-Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact Kähler manifolds.

  19. Geometry of Fractional Quantum Hall Fluids

    NASA Astrophysics Data System (ADS)

    Cho, Gil Young

    2015-03-01

    Fractional quantum Hall (FQH) fluids of two-dimensional electron gases (2DEG) in large magnetic fields are fascinating topological states of matter. As such they are characterized by universal properties such as their fractional quantum Hall conductivity, fractionally charged anyonic excitations and a degeneracy of topological origin on surfaces with the topology of a torus. Quite surprisingly these topological fluids also couple to the geometry on which the 2DEG resides and have universal responses to adiabatic changes in the geometry. These responses are given by a Wen-Zee term (which describes the coupling of the currents to the spin connection of the geometry) and a gravitational Chern-Simons term which reflects the universal energy and momentum transport along the edges of the FQH state. We use a field theory of the FQH states to derive these universal responses. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. Taking account of the framing anomaly of the quantum Chern-Simons theories, we derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both abelian and non-abelian states. This work was supported in part by the NSF Grant DMR-1408713.

  20. Topology Changing Transitions in Bubbling Geometries

    SciTech Connect

    Horava, Petr; Shepard, Peter G.

    2005-02-15

    Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

  1. Topology Changing Transitions in Bubbling Geometries

    SciTech Connect

    Horava, Petr; Shepard, Peter G.

    2005-02-15

    Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

  2. Pearson's Functions to Describe FSW Weld Geometry

    SciTech Connect

    Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.

    2011-01-17

    Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.

  3. Geometry optimization of branchings in vascular networks

    NASA Astrophysics Data System (ADS)

    Khamassi, Jamel; Bierwisch, Claas; Pelz, Peter

    2016-06-01

    Progress has been made in developing manufacturing technologies which enable the fabrication of artificial vascular networks for tissue cultivation. However, those networks are rudimentary designed with respect to their geometry. This restricts long-term biological functionality of vascular cells which depends on geometry-related fluid mechanical stimuli and the avoidance of vessel occlusion. In the present work, a bioinspired geometry optimization for branchings in artificial vascular networks has been conducted. The analysis could be simplified by exploiting self-similarity properties of the system. Design rules in the form of two geometrical parameters, i.e., the branching angle and the radius ratio of the daughter branches, are derived using the wall shear stress as command variable. The numerical values of these parameters are within the range of experimental observations. Those design rules are not only beneficial for tissue engineering applications. Moreover, they can be used as indicators for diagnoses of vascular diseases or for the layout of vascular grafts.

  4. Geometry of fractional quantum Hall fluids

    NASA Astrophysics Data System (ADS)

    Cho, Gil Young; You, Yizhi; Fradkin, Eduardo

    2014-09-01

    We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e., the Hall viscosity, and the Wen-Zee term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. We derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both Abelian and non-Abelian states.

  5. Interfacial geometry dictates cancer cell tumorigenicity

    NASA Astrophysics Data System (ADS)

    Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.

    2016-08-01

    Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.

  6. Gully geometry: what are we measuring?

    NASA Astrophysics Data System (ADS)

    Casalí, J.; Giménez, R.; Campo-Bescós, M. A.

    2015-07-01

    Much of the research on (ephemeral) gully erosion comprises the determination of the geometry of these eroded channels, especially their width and depth. This is not a simple task due to uncertainty generated by the wide range of variability in gully cross section shapes found in the field. However, in the literature, this uncertainty is not recognized so that no criteria for their measurement are indicated. The aim of this work is to make researchers aware of the ambiguity that arises when characterizing the geometry of an ephemeral gully and similar eroded channels. In addition, a measurement protocol is proposed with the ultimate goal of pooling criteria in future works. It is suggested that the geometry of a gully could be characterized through its mean equivalent width and mean equivalent depth, which, together with its length, define an "equivalent prismatic gully" (EPG). The latter would facilitate the comparison between different gullies.

  7. Supersymmetric geometries of IIA supergravity III

    NASA Astrophysics Data System (ADS)

    Gran, Ulf; Papadopoulos, George; von Schultz, Christian

    2016-06-01

    We find that (massive) IIA backgrounds that admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g2 instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.

  8. Interfacial geometry dictates cancer cell tumorigenicity.

    PubMed

    Lee, Junmin; Abdeen, Amr A; Wycislo, Kathryn L; Fan, Timothy M; Kilian, Kristopher A

    2016-08-01

    Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis. PMID:27043781

  9. GEMPAK: An arbitrary aircraft geometry generator

    NASA Technical Reports Server (NTRS)

    Stack, S. H.; Edwards, C. L. W.; Small, W. J.

    1977-01-01

    A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.

  10. Laws of granular solids: geometry and topology.

    PubMed

    DeGiuli, Eric; McElwaine, Jim

    2011-10-01

    In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables that describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions. PMID:22181138

  11. Quantum Monte Carlo simulations in novel geometries

    NASA Astrophysics Data System (ADS)

    Iglovikov, Vladimir

    Quantum Monte Carlo simulations are giving increasing insight into the physics of strongly interacting bosons, spins, and fermions. Initial work focused on the simplest geometries, like a 2D square lattice. Increasingly, modern research is turning to more rich structures such as honeycomb lattice of graphene, the Lieb lattice of the CuO2 planes of cuprate superconductors, the triangular lattice, and coupled layers. These new geometries possess unique features which affect the physics in profound ways, eg a vanishing density of states and relativistic dispersion ("Dirac point'') of a honeycomb lattice, frustration on a triangular lattice, and a flat bands on a Lieb lattice. This thesis concerns both exploring the performance of QMC algorithms on different geometries(primarily via the "sign problem'') and also applying those algorithms to several interesting open problems.

  12. Students' misconceptions and errors in transformation geometry

    NASA Astrophysics Data System (ADS)

    Ada, Tuba; Kurtuluş, Aytaç

    2010-10-01

    This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The subject of this study included 126 third-year students in the Department of Mathematics Education. Data were collected from a seven questions exam. This exam consisted of three procedural questions, two conceptual questions and two procedural-conceptual questions. In data analysis, a descriptor code key was used. When the students' overall performances were considered for all seven questions, the results showed that they did not understand how to apply rotation transformation. The mostly observed mistakes showed that the students seemed to know the algebraic meaning of translation and also rotation but they did not seem to understand the geometric meaning of them.

  13. Supersymmetric geometries of IIA supergravity III

    NASA Astrophysics Data System (ADS)

    Gran, Ulf; Papadopoulos, George; von Schultz, Christian

    2016-06-01

    We find that (massive) IIA backgrounds that admit a {G}_2ltimes {{R}}^8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g2 instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a {G}_2ltimes {{R}}^8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.

  14. Aspects of electrostatics in BTZ geometries

    NASA Astrophysics Data System (ADS)

    Herrera, Y.; Hurovich, V.; Santillán, O.; Simeone, C.

    2015-10-01

    In the present paper the electrostatics of charges in nonrotating BTZ black hole and wormhole spacetimes is studied. Our attention is focused on the self-force of a point charge in the geometry, for which a regularization prescription based on the Haddamard Green function is employed. The differences between the self-force in both cases is a theoretical experiment for distinguishing both geometries, which otherwise are locally indistinguishable. This idea was applied before to four and higher-dimensional black holes by the present and other authors. However, the particularities of the BTZ geometry makes the analysis considerable more complicated than those. First, the BTZ spacetimes are not asymptotically flat but instead asymptotically AdS. In addition, the relative distance d (r ,r +1 ) between two particles located at a radius r and r +1 in the geometry tends to zero when r →∞. This behavior, which is radically different in a flat geometry, changes the analysis of the asymptotic conditions for the electrostatic field. The other problem is that there exist several regularization methods other than the one we are employing, and there does not exist a proof in three dimensions that they are equivalent. However, we focus on the Haddamard method and obtain an expression for the hypothetical self-force in series, and the resulting expansion is convergent to the real solution. We suspect that the convergence is not uniform, and furthermore there are no summation formulas at our disposal. It appears, for points that are far away from the black hole the calculation of the Haddamard self-force requires higher-order summation. These subtleties are carefully analyzed in the paper, and it is shown that they lead to severe problems when calculating the Haddamard self-force for asymptotic points in the geometry.

  15. Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

    ERIC Educational Resources Information Center

    Guven, Bulent

    2012-01-01

    This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

  16. Performance on Middle School Geometry Problems with Geometry Clues Matched to Three Different Cognitive Styles

    ERIC Educational Resources Information Center

    Anderson, Karen L.; Casey, M. Beth; Thompson, William L.; Burrage, Marie S.; Pezaris, Elizabeth; Kosslyn, Stephen M.

    2008-01-01

    This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

  17. Coordinate Geometry. Geometry Module for Use in a Mathematics Laboratory Setting.

    ERIC Educational Resources Information Center

    Brotherton, Sheila; And Others

    This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module includes: (1) Pythagorean Theorem (with review of radicals); (2) Basic Coordinate Geometry (distance and midpoint, slope, slope of parallels and perpendiculars, and equation of a line); (3) Selecting Coordinates; (4) Coordinate…

  18. A tool for bistatic sar geometry determinations

    NASA Astrophysics Data System (ADS)

    Hawkins, R.; Gibson, J.; Antonik, P.; Saper, R.; Seymour, M.; St Hilaire, M.; Livingstone, C.

    The geometry of wide angle bistatic SAR is somewhat more complex than that of conventional SAR because the transmitter and receiver are displaced considerably. Constant bistatic range contours projected onto the geoid form ellipse-like profiles with the transmitter and receiver located at the two foci. Constant Doppler lines intersect the range ellipses and allow under special circumstances a simple orthogonal basis for processing and analysis. This paper illustrates a simple GUI- based tool developed in a MatLab that uses satellite orbit parameters and RADARSAT-1 data to simulate the bistatic geometry and scattering for a tower- based receiver.

  19. Effect of geometry on hydrodynamic film thickness

    NASA Technical Reports Server (NTRS)

    Brewe, D. E.; Hamrock, B. J.; Taylor, C. M.

    1978-01-01

    The influence of geometry on the isothermal hydrodynamic film separating two rigid solids was investigated. Pressure-viscosity effects were not considered. The minimum film thickness is derived for fully flooded conjunctions by using the Reynolds conditions. It was found that the minimum film thickness had the same speed, viscosity, and load dependence as Kapitza's classical solution. However, the incorporation of Reynolds boundary conditions resulted in an additional geometry effect. Solutions using the parabolic film approximation are compared with those using the exact expression for the film in the analysis. Contour plots are shown that indicate in detail the pressure developed between the solids.

  20. Thermal geometry from CFT at finite temperature

    NASA Astrophysics Data System (ADS)

    Gan, Wen-Cong; Shu, Fu-Wen; Wu, Meng-He

    2016-09-01

    We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking-Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  1. Congruent gridding for developable geometries using NURBS

    SciTech Connect

    Fritts, M.; Weems, K.

    1996-12-31

    This paper discusses recent progress in developing an interactive system built upon NURBS geometry modeling to ensure congruence of surface grids and surface geometries for structured and unstructured gridders. The code system is being developed as part of a collaborative effort among Nausea/Carderock Division, NASA/Lewis, Boeing Computer Services, and SAIC/Ship Technology Division, and uses the Navy library of NURBS FORTRAN subroutines, DT-NURBS, to allow incorporation into a wide variety of gridding codes and flow solvers. Although this paper will present examples relevant to the design of ship hulls only, the code system is being developed to support the design and manufacture of complex mechanical systems.

  2. SABRINA - an interactive geometry modeler for MCNP

    SciTech Connect

    West, J.T.; Murphy, J. )

    1988-01-01

    One of the most difficult tasks when analyzing a complex three-dimensional system with Monte Carlo is geometry model development. SABRINA attempts to make the modeling process more user-friendly and less of an obstacle. It accepts both combinatorial solid bodies and MCNP surfaces and produces MCNP cells. The model development process in SABRINA is highly interactive and gives the user immediate feedback on errors. Users can view their geometry from arbitrary perspectives while the model is under development and interactively find and correct modeling errors. An example of a SABRINA display is shown. It represents a complex three-dimensional shape.

  3. Fields and Laplacians on Quantum Geometries

    NASA Astrophysics Data System (ADS)

    Thürigen, Johannes

    2015-01-01

    In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.

  4. Radiation transport in dust in disk geometry

    NASA Technical Reports Server (NTRS)

    Chun, Ming Leung

    1986-01-01

    The main objective of the research program is twofold: (1) to develop a computer code to solve the problem of scattering, absorption and emission of photons by dust grains in a dusty medium with 2 dimensional disk geometry, and (2) to study the various physical and geometrical effects of 2 dimensional radiation transport on the thermal structure and radiation field. These tasks were accomplished and are briefly summarized. The method for solving the radiation transport problem in disk geometry is a generalization of the quasi-diffusion method (QDM) previously developed by the author.

  5. Modeling dynamical geometry with lattice gas automata

    SciTech Connect

    Hasslacher, B.; Meyer, D.A.

    1998-06-27

    Conventional lattice gas automata consist of particles moving discretely on a fixed lattice. While such models have been quite successful for a variety of fluid flow problems, there are other systems, e.g., flow in a flexible membrane or chemical self-assembly, in which the geometry is dynamical and coupled to the particle flow. Systems of this type seem to call for lattice gas models with dynamical geometry. The authors construct such a model on one dimensional (periodic) lattices and describe some simulations illustrating its nonequilibrium dynamics.

  6. Problems of Geophysics that Inspired Fractal Geometry

    NASA Astrophysics Data System (ADS)

    Mandelbrot, B. B.

    2001-12-01

    Fractal geometry arose when the speaker used then esoteric mathematics and the concept of invariance as a tool to understand diverse ``down-to-earth'' practical needs. The first step consisted in using discontinuous functions to represent the variation of speculative prices. The next several steps consisted in introducing infinite-range (global) dependence to handle data from geophysics, beginning with hydrology (and also again in finance). This talk will detail the speaker's debt and gratitude toward several specialists from diverse areas of geophysics who had the greatest impact on fractal geometry in its formative period.

  7. Method for Determining Optimum Injector Inlet Geometry

    NASA Technical Reports Server (NTRS)

    Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)

    2015-01-01

    A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.

  8. Information geometry and the renormalization group.

    PubMed

    Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata

    2015-11-01

    Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective. PMID:26651641

  9. Transversely Hessian foliations and information geometry

    NASA Astrophysics Data System (ADS)

    Boyom, Michel Nguiffo; Wolak, Robert

    2015-01-01

    A family of probability distributions parametrized by an open domain Λ in Rn defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix is positive definite defining in this way a Riemannian metric on Λ. If we replace the "positive definite" assumption by "0-deformable" condition a foliation with a transvesely Hessian structure appears naturally. We develop the study of transversely Hessian foliations in view of applications in information geometry.

  10. Information geometry and the renormalization group

    NASA Astrophysics Data System (ADS)

    Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata

    2015-11-01

    Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.

  11. Geometry and the Design of Product Packaging

    ERIC Educational Resources Information Center

    Cherico, Cindy M.

    2011-01-01

    The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

  12. Thermodynamic geometry and critical aspects of bifurcations

    NASA Astrophysics Data System (ADS)

    Mihara, A.

    2016-07-01

    This work presents an exploratory study of the critical aspects of some well-known bifurcations in the context of thermodynamic geometry. For each bifurcation its normal form is regarded as a geodesic equation of some model analogous to a thermodynamic system. From this hypothesis it is possible to calculate the corresponding metric and curvature and analyze the critical behavior of the bifurcation.

  13. Environment Study with Buckminster Fuller's Geometry

    ERIC Educational Resources Information Center

    Cohen, Martin J.; Petrillo, Joseph

    1972-01-01

    Describes the teaching of geodesic-dome concepts to students in grades 3-5 through the trial use of Energetic and Synergetic Geometry as well as the undertaking of a workshop designed to prepare elementary and secondary school teachers to conduct further experiments. (CC)

  14. User Interface Design for Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Kortenkamp, Ulrich; Dohrmann, Christian

    2010-01-01

    In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.

  15. Children's Use of Geometry for Reorientation

    ERIC Educational Resources Information Center

    Lee, Sang Ah; Spelke, Elizabeth S.

    2008-01-01

    Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the…

  16. Preparing for Formal Proofs in Geometry

    ERIC Educational Resources Information Center

    Johnson, Art

    2009-01-01

    One way in which geometry teachers can help students develop their reasoning is by providing proof-readiness experiences. Blum and Kirsch (1991) suggest that "preformal proofs" can help students develop deductive reasoning. Preformal proofs, which follow the basic principles of deductive reasoning, can help prepare students for formal deduction in…

  17. Effectiveness of Multimedia in Teaching Descriptive Geometry.

    ERIC Educational Resources Information Center

    Rankowski, Charles A.; Galey, Minaruth

    1979-01-01

    Demonstrates the instructional value of supplementary media presentations using first year engineering students randomly split into 11 descriptive geometry classes; five received multimedia instruction, and six did not. Data compared each study group in relation to competency in the subject, achievement, visualization of spatial relationships, and…

  18. Connecting Functions in Geometry and Algebra

    ERIC Educational Resources Information Center

    Steketee, Scott; Scher, Daniel

    2016-01-01

    One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

  19. Transport Code for Regular Triangular Geometry

    Energy Science and Technology Software Center (ESTSC)

    1993-06-09

    DIAMANT2 solves the two-dimensional static multigroup neutron transport equation in planar regular triangular geometry. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective or input specified boundary flux conditions are solved. Anisotropy is allowed for the scattering source. Volume and surface sources are allowed for inhomogeneous problems.

  20. Applications of Differential Geometry to Cartography

    ERIC Educational Resources Information Center

    Benitez, Julio; Thome, Nestor

    2004-01-01

    This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

  1. Geometry 3, Mathematics (Experimental): 5228.32.

    ERIC Educational Resources Information Center

    Josepher, Nelda; Temple, Aline

    This is the second of a two quin series which introduces the student to all the theorems usually included in high school geometry; emphasis is on understanding and use of these theorems without proof. The course develops definitions and properties of the plane and solid figures and formulates methods for finding their linear measure, lateral and…

  2. Quilts and Tangrams: Linking Literature and Geometry.

    ERIC Educational Resources Information Center

    Bohning, Gerry; Williams, Rebecca

    1997-01-01

    Suggests that by making quilt squares with tangrams, children link geometry and children's literature. Provides background on quilts and tangrams, and provides guidelines for teachers. Points out that children gain communication and mathematical thinking skills as they manipulate and explore relationships among pieces. Contains an annotated…

  3. The Geometry of the Universe: Part 1

    ERIC Educational Resources Information Center

    Francis, Stephanie

    2009-01-01

    This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…

  4. From Circle to Hyperbola in Taxicab Geometry

    ERIC Educational Resources Information Center

    Berger, Ruth I.

    2015-01-01

    This "Activity for Students" article presents a taxicab geometry problem that engages students in plotting points and observing surprising shapes and underlining reasons for the appearance of figures when working with street grids. With this activity, teachers can provide an extra challenge by writing additional problems introducing a…

  5. Geometry Success, Brain Theory, and Community Building

    ERIC Educational Resources Information Center

    Antink, Suzanne B. Loyer

    2010-01-01

    This action research project was aimed to improve geometry students' achievement and the retention in a suburban public high school over a one-year implementation cycle. The curricular design was influenced by Dweck's (2006) theories of growth mindset, educational standards, and directives outlined by the National Council of Teachers of…

  6. Learning Geometry by Designing Persian Mosaics

    ERIC Educational Resources Information Center

    Karssenberg, Goossen

    2014-01-01

    To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…

  7. The Valence Bond Interpretation of Molecular Geometry.

    ERIC Educational Resources Information Center

    Smith, Derek W.

    1980-01-01

    Presents ways in which the valence bond (VB) theory describes the bonding and geometry of molecules, following directly from earlier principles laid down by Pauling and others. Two other theories (molecular orbital approach and valence shell electron pair repulsion) are discussed and compared to VB. (CS)

  8. The Geometry of Newton's and Einstein's Theories

    NASA Astrophysics Data System (ADS)

    Hall, Graham S.

    The aim of this paper is to present a simple, brief, mathematical discussion of the interplay between geometry and physics in the theories of Newton and Einstein. The reader will be assumed to have some familiarity with classical Newtonian theory, the ideas of special and general relativity theory (and differential geometry), and the axiomatic formulation of Euclidean geometry. An attempt will be made to describe the relationship between Galileo's law of inertia (Newton's first law) and Euclid's geometry, which is based on the idea of Newtonian absolute time. Newton's second law and classical gravitation theory will then be introduced through the elegant idea of Cartan and his space-time connection and space metric. This space metric will then be used to introduce Minkowski's metric in special relativity and its subsequent generalization, by Einstein, to incorporate relativistic gravitational theory. The role of the principles of equivalence and covariance will also be discussed. Finally, a brief discussion of cosmology will be given. Stress will be laid on the (geometrical) concepts involved rather than the details of the mathematics, in so far as this is possible.

  9. Special Relativity as a Simple Geometry Problem

    ERIC Educational Resources Information Center

    de Abreu, Rodrigo; Guerra, Vasco

    2009-01-01

    The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

  10. Spadework Prior to Deduction in Geometry.

    ERIC Educational Resources Information Center

    Shaughnessy, J. Michael; Burger, William F.

    1985-01-01

    The five levels of the van Hiele theory are described. Then interviewing tasks designed to be presented to students in kindergarten through college are presented. Finally, responses from 14 interviews are discussed, with implications for teaching geometry. Extensive references are included. (MNS)

  11. Asynchronous event-based hebbian epipolar geometry.

    PubMed

    Benosman, Ryad; Ieng, Sio-Hoï; Rogister, Paul; Posch, Christoph

    2011-11-01

    Epipolar geometry, the cornerstone of perspective stereo vision, has been studied extensively since the advent of computer vision. Establishing such a geometric constraint is of primary importance, as it allows the recovery of the 3-D structure of scenes. Estimating the epipolar constraints of nonperspective stereo is difficult, they can no longer be defined because of the complexity of the sensor geometry. This paper will show that these limitations are, to some extent, a consequence of the static image frames commonly used in vision. The conventional frame-based approach suffers from a lack of the dynamics present in natural scenes. We introduce the use of neuromorphic event-based--rather than frame-based--vision sensors for perspective stereo vision. This type of sensor uses the dimension of time as the main conveyor of information. In this paper, we present a model for asynchronous event-based vision, which is then used to derive a general new concept of epipolar geometry linked to the temporal activation of pixels. Practical experiments demonstrate the validity of the approach, solving the problem of estimating the fundamental matrix applied, in a first stage, to classic perspective vision and then to more general cameras. Furthermore, this paper shows that the properties of event-based vision sensors allow the exploration of not-yet-defined geometric relationships, finally, we provide a definition of general epipolar geometry deployable to almost any visual sensor. PMID:21954205

  12. Honeycomb Geometry: Applied Mathematics in Nature.

    ERIC Educational Resources Information Center

    Roberts, William J.

    1984-01-01

    Study and exploration of the hexagonal shapes found in honeycombs is suggested as an interesting topic for geometry classes. Students learn that the hexagonal pattern maximizes the enclosed region and minimizes the wax needed for construction, while satisfying the bees' cell-size constraint. (MNS)

  13. Magnetic resonance spectra and statistical geometry

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate...

  14. Convex geometry analysis method of hyperspectral data

    NASA Astrophysics Data System (ADS)

    Gong, Yanjun; Wang, XiChang; Qi, Hongxing; Yu, BingXi

    2003-06-01

    We present matrix expression of convex geometry analysis method of hyperspectral data by linear mixing model and establish a mathematic model of endmembers. A 30-band remote sensing image is applied to testify the model. The results of analysis reveal that the method can analyze mixed pixel questions. The targets that are smaller than earth surface pixel can be identified by applying the method.

  15. Fostering Spatial vs. Metric Understanding in Geometry

    ERIC Educational Resources Information Center

    Kinach, Barbara M.

    2012-01-01

    Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

  16. Solving Geometry Problems via Mechanical Principles

    ERIC Educational Resources Information Center

    Man, Yiu Kwong

    2004-01-01

    The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…

  17. Project-Based Learning to Explore Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba; Kurtulus, Aytac

    2012-01-01

    In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…

  18. SABRINA: an interactive solid geometry modeling program for Monte Carlo

    SciTech Connect

    West, J.T.

    1985-01-01

    SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.

  19. van Hiele Levels and Achievement in Writing Geometry Proofs.

    ERIC Educational Resources Information Center

    Senk, Sharon L.

    1989-01-01

    Secondary geometry students were tested for van Hiele level of thinking, geometry knowledge and achievement, and proof-writing achievement. Proof-writing achievement correlated significantly with van Hiele level entering geometry knowledge and geometry achievement. The predictive validity of the van Hiele model was supported. (Author/DC)

  20. Modelling functional effects of muscle geometry.

    PubMed

    van der Linden, B J; Koopman, H F; Grootenboer, H J; Huijing, P A

    1998-04-01

    Muscle architecture is an important aspect of muscle functioning. Hence, geometry and material properties of muscle have great influence on the force-length characteristics of muscle. We compared experimental results for the gastrocnemius medialis muscle (GM) of the rat to model results of simple geometric models such as a planimetric model and three-dimensional versions of this model. The capabilities of such models to adequately calculate muscle geometry and force-length characteristics were investigated. The planimetric model with elastic aponeurosis predicted GM muscle geometry well: maximal differences are 6, 1, 4 and 6% for fiber length, aponeurosis length, fiber angle and aponeurosis angle respectively. A slanted cylinder model with circular fiber cross-section did not predict muscle geometry as well as the planimetric model, whereas the geometry results of a second slanted cylinder model were identical to the planimetric model. It is concluded that the planimetric model is capable of adequately calculating the muscle geometry over the muscle length range studied. However, for modelling of force-length characteristics more complex models are needed, as none of the models yielded results sufficiently close to experimental data. Modelled force-length characteristics showed an overestimation of muscle optimum length by 2 mm with respect to experimental data, and the force at the ascending limb of the length force curve was underestimated. The models presented neglect important aspects such as non-linear geometry of muscle, certain passive material properties and mechanical interactions of fibers. These aspects may be responsible for short-comings in the modelling. It is argued that, considering the inability to adequately model muscle length-force characteristics for an isolated maximally activated (in situ) muscle, it is to be expected that prediction will fail for muscle properties in conditions of complex movement with many interacting factors. Therefore

  1. Heterogeneity of coronary arterial branching geometry

    NASA Astrophysics Data System (ADS)

    Wan, Shu-Yen; Reyes, Denise A.; Higgins, William E.; Ritman, Erik L.

    2000-04-01

    Past measurements of arterial branching geometry have indicated that the branching geometry is somewhat consistent with an optimal trade-off between the work needed to build and maintain the arterial tree and the work needed to operate the tree as a transport system. The branching geometry is also consistent with the mechanism that acutely adjusts the lumen diameter by way of maintaining a constant shear stress by dilating (or constricting) the arteries via the nitric oxide mechanism. However, those observations also indicate that there is considerable variation about the predicted optimization, both within any one individual and between individuals. Possible causes for this variation include: (1) measurement noise -- both due to the imprecision of the method but also the preparation of the specimen for applying the measurement technique, (2) the fact that the measurement task presents a major logistic problem, which increases as the vessel size decreases (but the number of branches correspondingly doubles at each branching) and results in progressive under-sampling as the vessel size decreases, (3) because of the logistic task involved the number of arterial trees analyzed is also greatly limited, and (4) there may indeed be actual heterogeneity in the geometry which is due to slight variation in implementation of the 'rules' used to construct a vascular tree. Indeed, it is this latter possibility that is of considerable physiological interest as it could result in the observed heterogeneity of organ perfusion and also provide some insight into the relative importance of 'initial ' conditions (i.e., how the vascular tree initially develops during embryogenesis) and the adaptive mechanisms operative in the maturing individual. The use of micro-CT imaging to provide 3D images of the intact vascular tree within the intact organ overcomes or minimizes the logistic problems listed above. It is the purpose of this study to examine whether variability in the branching

  2. Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics

    ERIC Educational Resources Information Center

    Miyazaki, Mikio; Kimiho, Chino; Katoh, Ryuhei; Arai, Hitoshi; Ogihara, Fumihiro; Oguchi, Yuichi; Morozumi, Tatsuo; Kon, Mayuko; Komatsu, Kotaro

    2012-01-01

    Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…

  3. The Study of "Elementary Geometry" (1903) by Godfrey and Siddons (1): Roles of Experimental Tasks in the Teaching of Geometry.

    ERIC Educational Resources Information Center

    Fujita, Taro

    2001-01-01

    Examines the roles of experimental tasks in "Elementary Geometry" (1903) by Godfrey and Siddons, which is considered one of the most important geometry textbooks in the history of geometry teaching. Roles of experimental tasks included preparations for deductive geometry and, even though it is implicit, the verification of geometrical facts.…

  4. Predicting the Geometry Knowledge of Pre-Service Elementary Teachers (Sinif Ögretmeni Adaylarinin Geometri Bilgilerinin Yordanmasi)

    ERIC Educational Resources Information Center

    Duatepe Aksu, Asuman

    2013-01-01

    In this study, the aim was to examine the factors that predict the geometry knowledge of pre-service elementary teachers. Data was collected on 387 pre-service elementary teachers from four universities by using a geometry knowledge test, the van Hiele geometric thinking level test, a geometry self efficacy scale and a geometry attitude scale.…

  5. Automatic Conversion of Conceptual Geometry to CFD Geometry for Aircraft Design

    NASA Technical Reports Server (NTRS)

    Li, Wu

    2007-01-01

    Conceptual aircraft design is usually based on simple analysis codes. Its objective is to provide an overall system performance of the developed concept, while preliminary aircraft design uses high-fidelity analysis tools such as computational fluid dynamics (CFD) analysis codes or finite element structural analysis codes. In some applications, such as low-boom supersonic concept development, it is important to be able to explore a variety of drastically different configurations while using CFD analysis to check whether a given configuration can be tailored to have a low-boom ground signature. It poses an extremely challenging problem of integrating CFD analysis in conceptual design. This presentation will discuss a computer code, called iPatch, for automatic conversion of conceptual geometry to CFD geometry. In general, conceptual aircraft geometry is not as well-defined as a CAD geometry model. In particular, a conceptual aircraft geometry model usually does not define the intersection curves for the connecting surfaces. The computer code iPatch eliminates the gap between conceptual geometry and CFD geometry by accomplishing the following three tasks automatically: (1) use bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometry components (such as wing and fuselage) can be intersected to form a watertight CFD geometry, (2) compute the intersection curves of surface patches at any resolution (up to 10-7 accuracy) specified by users, and (3) write the B-spline surface patches and the corresponding boundary points for the watertight CFD geometry in the format that can be directly exported to the meshing tool VGRID in the CFD software TetrUSS. As a result, conceptual designers can get quick feedback on the aerodynamic characteristics of their concepts, which will allow them to understand some subtlety in their concepts and to be able to assess their concepts with a higher degree of

  6. Guiding chemical pulses through geometry: Y junctions.

    PubMed

    Qiao, L; Kevrekidis, I G; Punckt, C; Rotermund, H H

    2006-03-01

    We study computationally and experimentally the propagation of chemical pulses in complex geometries. The reaction of interest, CO oxidation, takes place on single crystal Pt(110) surfaces that are microlithographically patterned; they are also addressable through a focused laser beam, manipulated through galvanometer mirrors, capable of locally altering the crystal temperature and thus affecting pulse propagation. We focus on sudden changes in the domain shape (corners in a Y-junction geometry) that can affect the pulse dynamics; we also show how brief, localized temperature perturbations can be used to control reactive pulse propagation. The computational results are corroborated through experimental studies in which the pulses are visualized using reflection anisotropy microscopy. PMID:16605643

  7. A tool for bistatic SAR geometry determinations

    NASA Astrophysics Data System (ADS)

    Hawkins, R. K.; Gibson, J. R.; Saper, R.; Hilaire, M.

    2003-12-01

    The geometry of wide-angle bistatic Synthetic Aperture Radar (SAR) is somewhat more complex than that of conventional Synthetic Aperture Radar because the transmitter and receiver are displaced considerably. Constant bistatic range surfaces form ellipsoids, with the transmitter and receiver located at the two foci. These ellipsoids of constant bistatic range intersect the earth's surface in a series of ellipse-like contours. Constant Doppler lines intersect the range ellipses and allow, under special circumstances, a simple orthogonal basis for processing and analysis. This paper introduces a simple tool, developed in MatLab® and C++, that uses RADARSAT-1 as a satellite illuminator and a tower-based receiver. Actual orbit parameters and data from RADARSAT-1 are used in the simulation of the bistatic geometry and scattering.

  8. Shadow of noncommutative geometry inspired black hole

    NASA Astrophysics Data System (ADS)

    Wei, Shao-Wen; Cheng, Peng; Zhong, Yi; Zhou, Xiang-Nan

    2015-08-01

    In this paper, the shadow casted by the rotating black hole inspired by noncommutative geometry is investigated. In addition to the dimensionless spin parameter a/M0 with M0 black hole mass and inclination angle i, the dimensionless noncommutative parameter √vartheta/M0 is also found to affect the shape of the black hole shadow. The result shows that the size of the shadow slightly decreases with the parameter √vartheta/M0, while the distortion increases with it. Compared to the Kerr black hole, the parameter √vartheta/M0 increases the deformation of the shadow. This may offer a way to distinguish noncommutative geometry inspired black hole from Kerr one via astronomical instruments in the near future.

  9. Collective neutrino oscillations in nonspherical geometry

    SciTech Connect

    Dasgupta, Basudeb; Dighe, Amol; Mirizzi, Alessandro; Raffelt, Georg

    2008-08-01

    The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the nonspherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the 'single-angle approximation' frequently used for supernova neutrinos and allows for a natural generalization to nonspherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.

  10. Non-perturbative quantum geometry III

    NASA Astrophysics Data System (ADS)

    Krefl, Daniel

    2016-08-01

    The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kähler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local ℙ1 + ℙ1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local ℙ2 near the conifold point in moduli space is also provided.

  11. Downstream hydraulic geometry of alluvial rivers

    NASA Astrophysics Data System (ADS)

    Julien, P. Y.

    2015-03-01

    This article presents a three-level approach to the analysis of downstream hydraulic geometry. First, empirical concepts based on field observations of "poised" conditions in irrigation canals are examined. Second, theoretical developments have been made possible by combining basic relationships for the description of flow and sediment transport in alluvial rivers. Third, a relatively new concept of equivalent channel widths is presented. The assumption of equilibrium may describe a perpetual state of change and adjustments. The new concepts define the trade-offs between some hydraulic geometry parameters such as width and slope. The adjustment of river widths and slope typically follows a decreasing exponential function and recent developments indicate how the adjustment time scale can be quantified. Some examples are also presented to illustrate the new concepts presented and the realm of complex river systems.

  12. Geometry optimization in redundant internal coordinates

    NASA Astrophysics Data System (ADS)

    Pulay, P.; Fogarasi, G.

    1992-02-01

    The gradient geometry-optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton-Raphson-type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy-free internal coordinates. This procedure, already used for the geometry optimization of porphine, C20N4H14, is illustrated here at the ab initio self-consistent-field level for the four-membered ring azetidine, for bicyclo[2.2.2]octane, and for the four-ring system C16O2H22, the skeleton of taxol.

  13. Multiscale Talbot effects in Fibonacci geometry

    NASA Astrophysics Data System (ADS)

    Ho, I.-Lin; Chang, Yia-Chung

    2015-04-01

    This article investigates the Talbot effects in Fibonacci geometry by introducing the cut-and-projection construction, which allows for capturing the entire infinite Fibonacci structure in a single computational cell. Theoretical and numerical calculations demonstrate the Talbot foci of Fibonacci geometry at distances that are multiples (τ +2){{({{F}μ }+τ {{F}μ +1})}-1}p/(2q) or (τ +2){{({{L}μ }+τ {{L}μ +1})}-1}p/(2q) of the Talbot distance. Here (p, q) are coprime integers, μ is an integer, τ is the golden mean, and {{F}μ } and {{L}μ } are Fibonacci and Lucas numbers, respectively. The image of a single Talbot focus exhibits a multiscale-interval pattern due to the self-similarity of the scaling Fourier spectrum.

  14. Impacts of Conformational Geometries in Fluorinated Alkanes.

    PubMed

    Brandenburg, Tim; Golnak, Ronny; Nagasaka, Masanari; Atak, Kaan; Sreekantan Nair Lalithambika, Sreeju; Kosugi, Nobuhiro; Aziz, Emad F

    2016-01-01

    Research of blood substitute formulations and their base materials is of high scientific interest. Especially fluorinated microemulsions based on perfluorocarbons, with their interesting chemical properties, offer opportunities for applications in biomedicine and physical chemistry. In this work, carbon K-edge absorption spectra of liquid perfluoroalkanes and their parent hydrocarbons are presented and compared. Based on soft X-ray absorption, a comprehensive picture of the electronic structure is provided with the aid of time dependent density functional theory. We have observed that conformational geometries mainly influence the chemical and electronic interactions in the presented liquid materials, leading to a direct association of conformational geometries to the dissolving capacity of the presented perfluorocarbons with other solvents like water and possibly gases like oxygen. PMID:27527753

  15. Stages as models of scene geometry.

    PubMed

    Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark

    2010-09-01

    Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations. PMID:20634560

  16. Inductor Geometry With Improved Energy Density

    SciTech Connect

    Cui, H; Ngo, KDT; Moss, J; Lim, MHF; Rey, E

    2014-10-01

    The "constant-flux" concept is leveraged to achieve high magnetic-energy density, leading to inductor geometries with height significantly lower than that of conventional products. Techniques to shape the core and to distribute the winding turns to shape a desirable field profile are described for the two basic classes of magnetic geometries: those with the winding enclosed by the core and those with the core enclosed by the winding. A relatively constant flux distribution is advantageous not only from the density standpoint, but also from the thermal standpoint via the reduction of hot spots, and from the reliability standpoint via the suppression of flux crowding. In this journal paper on a constant-flux inductor (CFI) with enclosed winding, the foci are operating principle, dc analysis, and basic design procedure. Prototype cores and windings were routed from powder-iron disks and copper sheets, respectively. The design of CFI was validated by the assembled inductor prototype.

  17. Impacts of Conformational Geometries in Fluorinated Alkanes

    PubMed Central

    Brandenburg, Tim; Golnak, Ronny; Nagasaka, Masanari; Atak, Kaan; Sreekantan Nair Lalithambika, Sreeju; Kosugi, Nobuhiro; Aziz, Emad F.

    2016-01-01

    Research of blood substitute formulations and their base materials is of high scientific interest. Especially fluorinated microemulsions based on perfluorocarbons, with their interesting chemical properties, offer opportunities for applications in biomedicine and physical chemistry. In this work, carbon K-edge absorption spectra of liquid perfluoroalkanes and their parent hydrocarbons are presented and compared. Based on soft X-ray absorption, a comprehensive picture of the electronic structure is provided with the aid of time dependent density functional theory. We have observed that conformational geometries mainly influence the chemical and electronic interactions in the presented liquid materials, leading to a direct association of conformational geometries to the dissolving capacity of the presented perfluorocarbons with other solvents like water and possibly gases like oxygen. PMID:27527753

  18. Differential Geometry and Lie Groups for Physicists

    NASA Astrophysics Data System (ADS)

    Fecko, Marián.

    2011-03-01

    Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

  19. Differential Geometry and Lie Groups for Physicists

    NASA Astrophysics Data System (ADS)

    Fecko, Marián.

    2006-10-01

    Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

  20. Damage experiments in a cylindrical geometry

    SciTech Connect

    Kaul, Ann M

    2010-09-21

    Studying spallation damage with a cylindrical configuration allows for a natural recollection of the damaged material under proper driving conditions. Additionally, the damaged material can come to a complete rest without the application of further stopping forces. Specific areas of research include the damage initiation regime in convergent geometry, behavior of material recollected after damage, and effects of convergent geometry on the material response. Such experiments produce unique strain and shear stress states, motivating improvements in existing computational material models and increasing the predictive capabilities of codes. A LANL/VNIIEF joint experimental series has produced cylindrical aluminum failure initiation data and studied the behavior of material recollected after damage initiation and after complete failure. In addition to post-shot collection of the damaged target material for subsequent metallographic analysis, dynamic in-situ experimental diagnostics include velocimetry and transverse radial radiography. This paper will discuss the current experimental status.

  1. The universal instability in general geometry

    SciTech Connect

    Helander, P.; Plunk, G. G.

    2015-09-15

    The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.

  2. Extrinsic and intrinsic curvatures in thermodynamic geometry

    NASA Astrophysics Data System (ADS)

    Hosseini Mansoori, Seyed Ali; Mirza, Behrouz; Sharifian, Elham

    2016-08-01

    We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner-Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.

  3. Instabilities of microstate geometries with antibranes

    NASA Astrophysics Data System (ADS)

    Bena, Iosif; Pasini, Giulio

    2016-04-01

    One can obtain very large classes of horizonless microstate geometries corresponding to near-extremal black holes by placing probe supertubes whose action has metastable minima inside certain supersymmetric bubbling solutions [1]. We show that these minima can lower their energy when the bubbles move in certain directions in the moduli space, which implies that these near-extremal microstates are in fact unstable once one considers the dynamics of all their degrees of freedom. The decay of these solutions corresponds to Hawking radiation, and we compare the emission rate and frequency to those of the corresponding black hole. Our analysis supports the expectation that generic non-extremal black holes microstate geometries should be unstable. It also establishes the existence of a new type of instabilities for antibranes in highly-warped regions with charge dissolved in fluxes.

  4. Conformation Dependence of Backbone Geometry in Proteins

    PubMed Central

    Berkholz, Donald S.; Shapovalov, Maxim V.; Dunbrack, Roland L.; Karplus, P. Andrew

    2009-01-01

    Summary Protein structure determination and predictive modeling have long been guided by the paradigm that the peptide backbone has a single, context-independent ideal geometry. Both quantum-mechanics calculations and empirical analyses have shown this is an incorrect simplification in that backbone covalent geometry actually varies systematically as a function of the Φ and Ψ backbone dihedral angles. Here, we use a nonredundant set of ultrahigh-resolution protein structures to define these conformation-dependent variations. The trends have a rational, structural basis that can be explained by avoidance of atomic clashes or optimization of favorable electrostatic interactions. To facilitate adoption of this new paradigm, we have created a conformation-dependent library of covalent bond lengths and bond angles and shown that it has improved accuracy over existing methods without any additional variables to optimize. Protein structures derived both from crystallographic refinement and predictive modeling both stand to benefit from incorporation of the new paradigm. PMID:19836332

  5. A linguistic geometry for space applications

    NASA Technical Reports Server (NTRS)

    Stilman, Boris

    1994-01-01

    We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

  6. Robust optimisation of railway crossing geometry

    NASA Astrophysics Data System (ADS)

    Wan, Chang; Markine, Valeri; Dollevoet, Rolf

    2016-05-01

    This paper presents a methodology for improving the crossing (frog) geometry through the robust optimisation approach, wherein the variability of the design parameters within a prescribed tolerance is included in the optimisation problem. Here, the crossing geometry is defined by parameterising the B-spline represented cross-sectional shape and the longitudinal height profile of the nose rail. The dynamic performance of the crossing is evaluated considering the variation of wheel profiles and track alignment. A multipoint approximation method (MAM) is applied in solving the optimisation problem of minimising the contact pressure during the wheel-rail contact and constraining the location of wheel transition at the crossing. To clarify the difference between the robust optimisation and the normal deterministic optimisation approaches, the optimisation problems are solved in both approaches. The results show that the deterministic optimum fails under slight change of the design variables; the robust optimum, however, has improved and robust performance.

  7. Coaxial inverted geometry transistor having buried emitter

    NASA Technical Reports Server (NTRS)

    Hruby, R. J.; Cress, S. B.; Dunn, W. R. (Inventor)

    1973-01-01

    The invention relates to an inverted geometry transistor wherein the emitter is buried within the substrate. The transistor can be fabricated as a part of a monolithic integrated circuit and is particularly suited for use in applications where it is desired to employ low actuating voltages. The transistor may employ the same doping levels in the collector and emitter, so these connections can be reversed.

  8. The geometry of electron wave functions

    SciTech Connect

    Aminov, Yurii A

    2013-02-28

    To each wave function we assign a codimension-two submanifold in Euclidean space. We study the case of the wave function of a single electron in the hydrogen atom or other hydrogen-type atoms with quantum numbers n, l, m in detail. We prove theorems describing the behaviour of the scalar and sectional curvature of the constructed submanifold, depending on the quantum numbers. We also consider the external geometry of the submanifold. Bibliography: 9 titles.

  9. Linear stability of noncommutative spectral geometry

    NASA Astrophysics Data System (ADS)

    Sakellariadou, M.; Watcharangkool, A.

    2016-03-01

    We consider the spectral action within the context of a four-dimensional manifold with torsion and show that, in the vacuum case, the equations of motion reduce to Einstein's equations, securing the linear stability of the theory. To subsequently investigate the nonvacuum case, we consider the spectral action of an almost commutative torsion geometry and show that the Hamiltonian is bounded from below, a result which guarantees the linear stability of the theory.

  10. Testing R-parity with geometry

    NASA Astrophysics Data System (ADS)

    He, Yang-Hui; Jejjala, Vishnu; Matti, Cyril; Nelson, Brent D.

    2016-03-01

    We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new vacuum manifolds are identified; we thereby investigate the geometrical implication of theories which display a manifest matter parity (or R-parity) via the distinction between leptonic and Higgs doublets, and of the lepton number assignment of the right-handed neutrino fields.

  11. Extraction electrode geometry for a calutron

    DOEpatents

    Veach, A.M.; Bell, W.A. Jr.

    1975-09-23

    This patent relates to an improved geometry for the extraction electrode and the ground electrode utilized in the operation of a calutron. The improved electrodes are constructed in a partial-picture-frame fashion with the slits of both electrodes formed by two tungsten elongated rods. Additional parallel spaced-apart rods in each electrode are used to establish equipotential surfaces over the rest of the front of the ion source. (auth)

  12. Analytic Coleman-de Luccia Geometries

    SciTech Connect

    Dong, Xi; Harlow, Daniel; /Stanford U., ITP /Stanford U., Phys. Dept.

    2012-02-16

    We present the necessary and sufficient conditions for a Euclidean scale factor to be a solution of the Coleman-de Luccia equations for some analytic potential V ({psi}), with a Lorentzian continuation describing the growth of a bubble of lower-energy vacuum surrounded by higher-energy vacuum. We then give a set of explicit examples that satisfy the conditions and thus are closed-form analytic examples of Coleman-de Luccia geometries.

  13. Casimir energies of cavities: The geometry question

    NASA Astrophysics Data System (ADS)

    Abalo, Iroko Komi Elom

    The question of how the Casimir effect relates to a system's geometry is of fundamental interest. In this thesis, we present new results for interior Casimir self-energies of various integrable geometries and show interesting systematic relations between these energies. In particular, we consider prisms with triangular cross sections (equilateral, hemiequilateral, and right isosceles triangles), triangular polygons of the same cross sections, and three tetrahedra. The triangular prisms are of infinite or finite lengths. These geometries are integrable and unique in the sense that the Laplacian eigenvalues may be found using the method of images. We obtain interior Casimir energies for these cavities subject to Dirichlet and Neumann boundary conditions. In addition to these boundary conditions, we also obtain electromagnetic Casimir energies for the infinite prisms. These energies are regularized using various consistent methods, one of which is regularization by point-splitting. Summing these modes explicitly using a cylinder kernel formulation, we show that the correct Weyl divergences are obtained. We also give closed-form results for the infinite triangular prisms. In order to understand the geometry dependence of these energies, we rederive well-known results for rectangular parallelepipeds (including the cube) and infinite rectangular prisms. The analysis of these self-energies yields intriguing results. By plotting the scaled energies against the appropriately chosen isoperimetric or isoareal quotients, we observe interesting patterns, which hint towards a systematic functional dependence. In addition to the calculation of new Casimir energies, this constitutes a significant contribution to the theoretical understanding of self-energies and has interesting implications.

  14. Geometry and groups for cosmic topology

    SciTech Connect

    Kramer, Peter

    2011-03-21

    The Cosmic Microwave Background is measured by satellite observation with great precision. It offers insight into its origin in early states of the universe. Unexpected low multipole amplitudes of the incoming CMB radiation may be due to a multiply connected topology of cosmic 3-space. We present and analyze the geometry and homotopy for the family of Platonic spherical 3-manifolds, provide their harmonic analysis, and formulate topological selection rules.

  15. Damage experiments in cylindrical geometry update

    SciTech Connect

    Kaul, Anne; Holtkamp, David; Rodriguez, George

    2009-01-01

    Using a cylindrical configuration to study spallation damage allows for a natural recollection of the damaged material under proper driving conditions. Previous experiments provided data about failure initiation in aluminum in a cylindrical geometry and the behavior of material recollected after damage from pressures in the damage initiation regime. The current series of experiments studied the behavior of material recollected after complete failure. Results from the current experiments will be presented.

  16. Geometry of Quantum Computation with Qudits

    PubMed Central

    Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

    2014-01-01

    The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

  17. Intersecting solitons, amoeba, and tropical geometry

    SciTech Connect

    Fujimori, Toshiaki; Nitta, Muneto; Ohta, Kazutoshi; Sakai, Norisuke; Yamazaki, Masahito

    2008-11-15

    We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol'nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(N{sub C}) gauge theory on R{sub t}x(C*){sup 2}{approx_equal}R{sup 2,1}xT{sup 2} with N{sub F}=N{sub C} Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (N{sub F}=N{sub C}=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortex charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C*){sup 2}. The Wilson loops in T{sup 2} are related with derivatives of the Ronkin function. The general form of the Kaehler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.

  18. Geometry of guanidinium groups in arginines.

    PubMed

    Malinska, Maura; Dauter, Miroslawa; Dauter, Zbigniew

    2016-09-01

    The restraints in common usage today have been obtained based on small molecule X-ray crystal structures available 25 years ago and recent reports have shown that the values of bond lengths and valence angles can be, in fact, significantly different from those stored in libraries, for example for the peptide bond or the histidine ring geometry. We showed that almost 50% of outliers found in protein validation reports released in the Protein Data Bank on 23 March 2016 come from geometry of guanidine groups in arginines. Therefore, structures of small molecules and atomic resolution protein crystal structures have been used to derive new target values for the geometry of this group. The most significant difference was found for NE-CZ-NH1 and NE-CZ-NH2 angles, showing that the guanidinium group is not symmetric. The NE-CZ-NH1 angle is larger, 121.5(10)˚, than NE-CZ-NH2, 119.2(10)˚, due to the repulsive interaction between NH1 and CD1 atom. PMID:27326702

  19. RGG: Reactor geometry (and mesh) generator

    SciTech Connect

    Jain, R.; Tautges, T.

    2012-07-01

    The reactor geometry (and mesh) generator RGG takes advantage of information about repeated structures in both assembly and core lattices to simplify the creation of geometry and mesh. It is released as open source software as a part of the MeshKit mesh generation library. The methodology operates in three stages. First, assembly geometry models of various types are generated by a tool called AssyGen. Next, the assembly model or models are meshed by using MeshKit tools or the CUBIT mesh generation tool-kit, optionally based on a journal file output by AssyGen. After one or more assembly model meshes have been constructed, a tool called CoreGen uses a copy/move/merge process to arrange the model meshes into a core model. In this paper, we present the current state of tools and new features in RGG. We also discuss the parallel-enabled CoreGen, which in several cases achieves super-linear speedups since the problems fit in available RAM at higher processor counts. Several RGG applications - 1/6 VHTR model, 1/4 PWR reactor core, and a full-core model for Monju - are reported. (authors)

  20. Discovering Structural Regularity in 3D Geometry

    PubMed Central

    Pauly, Mark; Mitra, Niloy J.; Wallner, Johannes; Pottmann, Helmut; Guibas, Leonidas J.

    2010-01-01

    We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis. PMID:21170292

  1. Core systems of geometry in animal minds.

    PubMed

    Spelke, Elizabeth S; Lee, Sang Ah

    2012-10-01

    Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds. PMID:22927577

  2. Geometry-free linear combinations for Galileo

    NASA Astrophysics Data System (ADS)

    Henkel, Patrick

    2009-11-01

    Global navigation satellites of the European Galileo system transmit code signals on four carriers in the L1, E5a, E5b and E6 band. New geometry-free linear combinations are presented that eliminate the geometry terms (user to satellite ranges and orbital errors), the clock errors of the user and satellites and the tropospheric delay. The remaining parameters of these carrier phase combinations include integer ambiguities, ionospheric delays, carrier phase multipath and phase noise. The weighting coefficients are designed such that the integer nature of ambiguities is maintained. The use of four frequency combinations is highly recommended due to a noise reduction of up to 14.4 dB and an ionospheric reduction of up to 25.6 dB compared to two frequency geometry-free combinations. Moreover, a modified Least-squares Ambiguity Decorrelation Adjustment (LAMBDA) algorithm is suggested, which differs in two points from the traditional approach: the baseline is replaced by the ionospheric delay and the correlation is caused by linear combinations instead of double differences. For correct ambiguity resolution, the ionospheric delay can be determined with millimeter accuracy. This is quite beneficial as the ionosphere represents the largest source of error for absolute positioning.

  3. An elementary discussion of propellant flame geometry

    SciTech Connect

    Buckmaster, J.; Jackson, T.L.; Yao, J.

    1999-05-01

    The authors examine the geometry of diffusion flames generated by the burning of a heterogeneous solid propellant, using a simple model designed to provide qualitative insights. In the fast chemistry limit a strategy is used which has its roots in Burke and Schumann`s 1928 study of diffusion flames, albeit with different boundary conditions. This shows that the stoichiometric level surface (SLS) intersects the propellant surface at a point displaced from the fuel/oxidizer interface, and the variations of this displacement with Peclet number are discussed. The authors show that for model sandwich propellants, or their axisymmetric counterpart, the geometry of the SLS when the core is oxidizer is quite different from the geometry of the SLS when the core is fuel. Also, it is much easier to quench the flame on an oxidizer core, by reducing the Peclet number, than it is to quench the flame on a fuel core. When finite chemistry effects are accounted for, the flame only occupies a portion of the SLS, and there is a leading edge structure in which premixing plays a role. Enhancement of the burning rate due to premixing is identified, but a well-defined tribrachial structure is not observed. The authors show how a sharp reduction in pressure can lead to a detachment of the flame from the SLS, with subsequent quenching as it is swept downstream.

  4. Chiral geometry in multiple chiral doublet bands

    NASA Astrophysics Data System (ADS)

    Zhang, Hao; Chen, Qibo

    2016-02-01

    The chiral geometry of multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters γ in the particle rotor model with . The energy spectra, electromagnetic transition probabilities B(M1) and B(E2), angular momenta, and K-distributions are studied. It is demonstrated that the chirality still remains not only in the yrast and yrare bands, but also in the two higher excited bands when γ deviates from 30°. The chiral geometry relies significantly on γ, and the chiral geometry of the two higher excited partner bands is not as good as that of the yrast and yrare doublet bands. Supported by Plan Project of Beijing College Students’ Scientific Research and Entrepreneurial Action, Major State 973 Program of China (2013CB834400), National Natural Science Foundation of China (11175002, 11335002, 11375015, 11461141002), National Fund for Fostering Talents of Basic Science (NFFTBS) (J1103206), Research Fund for Doctoral Program of Higher Education (20110001110087) and China Postdoctoral Science Foundation (2015M580007)

  5. Core systems of geometry in animal minds

    PubMed Central

    Spelke, Elizabeth S.; Lee, Sang Ah

    2012-01-01

    Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds. PMID:22927577

  6. Interactions between pool geometry and hydraulics

    USGS Publications Warehouse

    Thompson, D.M.; Nelson, J.M.; Wohl, E.E.

    1998-01-01

    An experimental and computational research approach was used to determine interactions between pool geometry and hydraulics. A 20-m-long, 1.8-m-wide flume was used to investigate the effect of four different geometric aspects of pool shape on flow velocity. Plywood sections were used to systematically alter constriction width, pool depth, pool length, and pool exit-slope gradient, each at two separate levels. Using the resulting 16 unique geometries with measured pool velocities in four-way factorial analyses produced an empirical assessment of the role of the four geometric aspects on the pool flow patterns and hence the stability of the pool. To complement the conclusions of these analyses, a two-dimensional computational flow model was used to investigate the relationships between pool geometry and flow patterns over a wider range of conditions. Both experimental and computational results show that constriction and depth effects dominate in the jet section of the pool and that pool length exhibits an increasing effect within the recirculating-eddy system. The pool exit slope appears to force flow reattachment. Pool length controls recirculating-eddy length and vena contracta strength. In turn, the vena contracta and recirculating eddy control velocities throughout the pool.

  7. Control system for variable geometry turbocharger

    SciTech Connect

    Abo, T.; Ueno, T.; Sumizawa, A.

    1987-08-11

    A control system is described for a variable geometry turbocharger for an internal combustion engine including a turbine having a variable area inflow passage, the turbine being operated in response to an exhaust gas flow supplied through the variable area inflow passage, and a compressor adapted to be driven by the turbine. The control system consists of means for detecting operating conditions of the engine, a control means including arithmetic means which calculates a first control value for controlling the cross-sectional area of the variable area inflow passage to provide a suitable supercharging pressure of intake air supplied to the engine in response to the detected operating conditions of the engine, a first variable geometry valve means for changing the cross-sectional area of the variable area inflow passage, means for actuating the variable geometry valve means in accordance with the first control value; and a limiter means for changing the first control value so as to restrict a reduction of the cross sectional area of the variable area inflow passage when the calculated control value has reached a predetermined value after being changed to reduce the cross-sectional area of the variable area inflow passage.

  8. SPICE Supports Planetary Science Observation Geometry

    NASA Astrophysics Data System (ADS)

    Hall Acton, Charles; Bachman, Nathaniel J.; Semenov, Boris V.; Wright, Edward D.

    2015-11-01

    "SPICE" is an information system, comprising both data and software, providing scientists with the observation geometry needed to plan observations from instruments aboard robotic spacecraft, and to subsequently help in analyzing the data returned from those observations. The SPICE system has been used on the majority of worldwide planetary exploration missions since the time of NASA's Galileo mission to Jupiter. Along with its "free" price tag, portability and the absence of licensing and export restrictions, its stable, enduring qualities help make it a popular choice. But stability does not imply rigidity-improvements and new capabilities are regularly added. This poster highlights recent additions that could be of interest to planetary scientists.Geometry Finder allows one to find all the times or time intervals when a particular geometric condition exists (e.g. occultation) or when a particular geometric parameter is within a given range or has reached a maximum or minimum.Digital Shape Kernel (DSK) provides means to compute observation geometry using accurately modeled target bodies: a tessellated plate model for irregular bodies and a digital elevation model for large, regular bodies.WebGeocalc (WGC) provides a graphical user interface (GUI) to a SPICE "geometry engine" installed at a mission operations facility, such as the one operated by NAIF. A WGC user need have only a computer with a web browser to access this geometry engine. Using traditional GUI widgets-drop-down menus, check boxes, radio buttons and fill-in boxes-the user inputs the data to be used, the kind of calculation wanted, and the details of that calculation. The WGC server makes the specified calculations and returns results to the user's browser.Cosmographia is a mission visualization program. This tool provides 3D visualization of solar system (target) bodies, spacecraft trajectory and orientation, instrument field-of-view "cones" and footprints, and more.The research described in this

  9. Dynamic geometry, brain function modeling, and consciousness.

    PubMed

    Roy, Sisir; Llinás, Rodolfo

    2008-01-01

    Pellionisz and Llinás proposed, years ago, a geometric interpretation towards understanding brain function. This interpretation assumes that the relation between the brain and the external world is determined by the ability of the central nervous system (CNS) to construct an internal model of the external world using an interactive geometrical relationship between sensory and motor expression. This approach opened new vistas not only in brain research but also in understanding the foundations of geometry itself. The approach named tensor network theory is sufficiently rich to allow specific computational modeling and addressed the issue of prediction, based on Taylor series expansion properties of the system, at the neuronal level, as a basic property of brain function. It was actually proposed that the evolutionary realm is the backbone for the development of an internal functional space that, while being purely representational, can interact successfully with the totally different world of the so-called "external reality". Now if the internal space or functional space is endowed with stochastic metric tensor properties, then there will be a dynamic correspondence between events in the external world and their specification in the internal space. We shall call this dynamic geometry since the minimal time resolution of the brain (10-15 ms), associated with 40 Hz oscillations of neurons and their network dynamics, is considered to be responsible for recognizing external events and generating the concept of simultaneity. The stochastic metric tensor in dynamic geometry can be written as five-dimensional space-time where the fifth dimension is a probability space as well as a metric space. This extra dimension is considered an imbedded degree of freedom. It is worth noticing that the above-mentioned 40 Hz oscillation is present both in awake and dream states where the central difference is the inability of phase resetting in the latter. This framework of dynamic

  10. A proposal of an open PET geometry.

    PubMed

    Yamaya, Taiga; Inaniwa, Taku; Minohara, Shinichi; Yoshida, Eiji; Inadama, Naoko; Nishikido, Fumihiko; Shibuya, Kengo; Lam, Chih Fung; Murayama, Hideo

    2008-02-01

    The long patient port of a PET scanner tends to put stress on patients, especially patients with claustrophobia. It also prevents doctors and technicians from taking care of patients during scanning. In this paper, we proposed an 'open PET' geometry, which consists of two axially separated detector rings. A long and continuous field-of-view (FOV) including a 360 degrees opened gap between two detector rings can be imaged enabling a fully 3D image reconstruction of all the possible lines-of-response. The open PET will become practical if iterative image reconstruction methods are applied even though image reconstruction of the open PET is analytically an incomplete problem. First we implemented a 'masked' 3D ordered subset expectation maximization (OS-EM) in which the system matrix was obtained from a long 'gapless' scanner by applying a mask to detectors corresponding to the open space. Next, in order to evaluate imaging performance of the proposed open PET geometry, we simulated a dual HR+ scanner (ring diameter of D = 827 mm, axial length of W = 154 mm x 2) separated by a variable gap. The gap W was the maximum limit to have axially continuous FOV of 3W though the maximum diameter of FOV at the central slice was limited to D/2. Artifacts, observed on both sides of the open space when the gap exceeded W, were effectively reduced by inserting detectors partially into unnecessary open spaces. We also tested the open PET geometry using experimental data obtained by the jPET-D4. The jPET-D4 is a prototype brain scanner, which has 5 rings of 24 detector blocks. We simulated the open jPET-D4 with a gap of 66 mm by eliminating 1 block-ring from experimental data. Although some artifacts were seen at both ends of the opened gap, very similar images were obtained with and without the gap. The proposed open PET geometry is expected to lead to realization of in-beam PET, which is a method for an in situ monitoring of charged particle therapy, by letting the beams pass

  11. Geometry of loop quantum gravity on a graph

    SciTech Connect

    Rovelli, Carlo; Speziale, Simone

    2010-08-15

    We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the 'twisted geometries' and derive a simple relation between these and Regge geometries.

  12. Characterizing student mathematics teachers' levels of understanding in spherical geometry

    NASA Astrophysics Data System (ADS)

    Guven, Bulent; Baki, Adnan

    2010-12-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, task-based interviews were held with eight student mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean geometry.

  13. Developing the concept of a parabola in Taxicab geometry

    NASA Astrophysics Data System (ADS)

    Ada, Tuba; Kurtuluş, Aytaç; Bahadır Yanik, H.

    2015-02-01

    The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student. According to the findings, once the student learnt the definition of a parabola in Euclidean geometry, she was able to define a Taxicab parabola using the distance function in Taxicab geometry. Also, she came up with an algebraic definition of a Taxicab parabola based on this geometric definition of the concept of a parabola. Moving from algebraic definition to geometric representation, she configured the concept of a parabola in Taxicab geometry. By means of this application activity, the student had the opportunity to observe and practise the concept of a parabola in a real-life situation based on Euclidean geometry and Taxicab geometry.

  14. Introducing GV : The Spacecraft Geometry Visualizer

    NASA Astrophysics Data System (ADS)

    Throop, Henry B.; Stern, S. A.; Parker, J. W.; Gladstone, G. R.; Weaver, H. A.

    2009-12-01

    GV (Geometry Visualizer) is a web-based program for planning spacecraft observations. GV is the primary planning tool used by the New Horizons science team to plan the encounter with Pluto. GV creates accurate 3D images and movies showing the position of planets, satellites, and stars as seen from an observer on a spacecraft or other body. NAIF SPICE routines are used throughout for accurate calculations of all geometry. GV includes 3D geometry rendering of all planetary bodies, lon/lat grids, ground tracks, albedo maps, stellar magnitudes, types and positions from HD and Tycho-2 catalogs, and spacecraft FOVs. It generates still images, animations, and geometric data tables. GV is accessed through an easy-to-use and flexible web interface. The web-based interface allows for uniform use from any computer and assures that all users are accessing up-to-date versions of the code and kernel libraries. Compared with existing planning tools, GV is often simpler, faster, lower-cost, and more flexible. GV was developed at SwRI to support the New Horizons mission to Pluto. It has been subsequently expanded to support multiple other missions in flight or under development, including Cassini, Messenger, Rosetta, LRO, and Juno. The system can be used to plan Earth-based observations such as occultations to high precision, and was used by the public to help plan 'Kodak Moment' observations of the Pluto system from New Horizons. Potential users of GV may contact the author for more information. Development of GV has been funded by the New Horizons, Rosetta, and LRO missions.

  15. PREFACE: Algebra, Geometry, and Mathematical Physics 2010

    NASA Astrophysics Data System (ADS)

    Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.

    2012-02-01

    This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants

  16. Geometry and kinematic evolution of inversion structures

    SciTech Connect

    Mitra, S. )

    1993-07-01

    Positive inversion structures form by the compressional reactivation of preexisting extensional structures. Experimental models and observations of natural structures are used to develop quantitative models for the geometry and kinematic evolution of inversion structures. In this paper, I analyze two main formation mechanisms of inversion structures: (1) fault-propagation folding on planar faults, and (2) fault-bend folding on listric faults. Inversion structures formed by fault-propagation folding occur in the southern North Sea, the Central Montana platform, and the Kangean Basin. During extension, a broad fault-propagation (or drape) fold develops above the master fault, with the fault subsequently breaking through the fold. Synextensional growth units deposited in the hanging wall typically thicken into the basin. Compressional reactivation results in slip reversal on the master and secondary faults, their rotation to shallower dips, and the development of a compressional fault-propagation fold. Inversion structures formed by fault-bend folding on listric faults occur in the Taranaki Basin, and possibly in the southern North Sea. Rollover folding in the hanging wall occurs during extension, possibly accompanied by a small component of fault-propagation folding in the vicinity of the fault tip. Deformation is primarily along a system of antithetic faults. Synextensional growth sediments typically thicken into the fault, but also show thinning in the immediate vicinity of the fault. During compression, the extensional fold is first unfolded and then folded into a compressional fault-bend fold. The characteristic variations in bed geometry and thickness provide predictive models for interpreting the subsurface geometries of these two classes of inversion structures in areas with poor seismic data. These models are particularly useful in exploring for structural traps in the complex and relatively unexplored synextensional growth units. 31 refs., 29 figs.

  17. Electronic hidden solder joint geometry characterization

    NASA Astrophysics Data System (ADS)

    Hsieh, Sheng-Jen

    2009-05-01

    To reduce the size of electronic equipment, multi-layer printed circuit board structures have become popular in recent years. As a result, the inspection of hidden solder joints between layers of boards has become increasingly difficult. Xray machines have been used for ball grid array (BGA) and hidden solder joint inspection; however, the equipment is costly and the inspection process is time consuming. In this paper, we investigate an active thermography approach to probing solder joint geometry. A set of boards having the same number of solder joints and amount of solder paste (0.061 g) was fabricated. Each solder joint had a different geometry. A semi-automated system was built to heat and then transfer each board to a chamber where an infrared camera was used to scan the board as it was cooling down. Two-thirds of the data set was used for model development and one-third was used for model evaluation. Both artificial neural network (ANN) and binary logistic regression models were constructed. Results suggest that solder joints with more surface area cool much faster than those with less surface area. In addition, both modeling approaches are consistent in predicting solder geometry; ANN had 85% accuracy and the regression model had 80%. This approach can potentially be used to test for cold solder joints prior to BGA assembly, since cold solder joints may have air gaps between the joint and the board and air is a poor heat conductor. Therefore, a cold solder joint may have a slower cooling rate than a normal one.

  18. Cloud geometry effects on atmospheric solar absorption

    SciTech Connect

    Fu, Q.; Cribb, M.C.; Barker, H.W.; Krueger, S.K.; Grossman, A.

    2000-04-15

    A 3D broadband solar radiative transfer scheme is formulated by integrating a Monte Carlo photon transport algorithm with the Fu-Liou radiation model. It is applied to fields of tropical mesoscale convective clouds and subtropical marine boundary layer clouds that were generated by a 2D cloud-resolving model. The effects of cloud geometry on the radiative energy budget are examined by comparing the full-resolution Monte Carlo results with those from the independent column approximation (ICA) that applies the plane-parallel radiation model to each column. For the tropical convective cloud system, it is found that cloud geometry effects always enhance atmospheric solar absorption regardless of solar zenith angle. In a large horizontal domain (512 km), differences in domain-averaged atmospheric absorption between the Monte Carlo and the ICA are less than 4 W m{sup {minus}2} in the daytime. However, for a smaller domain (e.g., 75 km) containing a cluster of deep convective towers, domain-averaged absorption can be enhanced by more than 20 W m{sup {minus}2}. For a subtropical marine boundary layer cloud system during the stratus-to-cumulus transition, calculations show that the ICA works very well for domain-averaged fluxes of the stratocumulus cloud fields even for a very small domain (4.8 km). For the trade cumulus cloud field, the effects of cloud sides and horizontal transport of photons become more significant. Calculations have also been made for both cloud systems including black carbon aerosol and a water vapor continuum. It is found that cloud geometry produces no discernible effects on the absorption enhancement due to the black carbon aerosol and water vapor continuum. The current study indicates that the atmospheric absorption enhancement due to cloud-related 3D photon transport is small. This enhancement could not explain the excess absorption suggested by recent studies.

  19. BTZ black holes inspired by noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Rahaman, Farook; Kuhfittig, P. K. F.; Bhui, B. C.; Rahaman, Mosiur; Ray, Saibal; Mondal, U. F.

    2013-04-01

    In this paper, a Bañados-Teitelboim-Zanelli (BTZ) black hole [Phys. Rev. Lett. 69, 1849 (1992)] is constructed from an exact solution of the Einstein field equations in a (2+1)—dimensional anti—de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have either two horizons, no horizon, or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy, and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible.

  20. Differential geometry, Palatini gravity and reduction

    SciTech Connect

    Capriotti, S.

    2014-01-15

    The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle LM are used. A generalization of Lagrange-Poincaré reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.

  1. Ring geometry on Ganymede and Callisto

    NASA Technical Reports Server (NTRS)

    Schenk, Paul M.; Mckinnon, William B.

    1987-01-01

    Geometrical considerations are brought to bear on a discussion of the impact and internal origin scenarios for the major furrow system of Ganymede, which was remapped in order to take advantage of improvements in coordinate control. Furrow occurrence and geometry are judged to be consistent with an impact origin; the perceived current nonalignment of the presumably once-concentric furrows may be adduced as evidence for large-scale lateral motion of dark terrain blocks in Ganymede's crust, in association with bright terrain formation.

  2. Drift Mode Calculations in Nonaxisymmetric Geometry

    SciTech Connect

    G. Rewoldt; L.-P. Ku; W.A. Cooper; W.M. Tang

    1999-07-01

    A fully kinetic assessment of the stability properties of toroidal drift modes has been obtained for nonaxisymmetric (stellarator) geometry, in the electrostatic limit. This calculation is a comprehensive solution of the linearized gyrokinetic equation, using the lowest-order ''ballooning representation'' for high toroidal mode number instabilities, with a model collision operator. Results for toroidal drift waves destabilized by temperature gradients and/or trapped particle dynamics are presented, using three-dimensional magnetohydrodynamic equilibria generated as part of a design effort for a quasiaxisymmetric stellarator. Comparisons of these results with those obtained for typical tokamak cases indicate that the basic trends are similar.

  3. GGADT: Generalized Geometry Anomalous Diffraction Theory

    NASA Astrophysics Data System (ADS)

    Hoffman, John; Tarczon, Michael; Draine, Bruce T.

    2015-10-01

    GGADT uses anomalous diffraction theory (ADT) to compute the differential scattering cross section (or the total cross sections as a function of energy) for a specified grain of arbitrary geometry (natively supports spheres, ellipsoids, and clusters of spherical monomers). It is written in Fortran 95. ADT is valid when the grain is large compared to the wavelength of incident light. GGADT can calculate either the integrated cross sections (absorption, scattering, extinction) as a function of energy, or it can calculate the differential scattering cross section as a function of scattering angle.

  4. Numerical quadrature for slab geometry transport algorithms

    SciTech Connect

    Hennart, J.P.; Valle, E. del

    1995-12-31

    In recent papers, a generalized nodal finite element formalism has been presented for virtually all known linear finite difference approximations to the discrete ordinates equations in slab geometry. For a particular angular directions {mu}, the neutron flux {Phi} is approximated by a piecewise function Oh, which over each space interval can be polynomial or quasipolynomial. Here we shall restrict ourselves to the polynomial case. Over each space interval, {Phi} is a polynomial of degree k, interpolating parameters given by in the continuous and discontinuous cases, respectively. The angular flux at the left and right ends and the k`th Legendre moment of {Phi} over the cell considered are represented as.

  5. The Local Geometry of Multiattribute Tradeoff Preferences

    PubMed Central

    McGeachie, Michael; Doyle, Jon

    2011-01-01

    Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes. PMID:21528018

  6. The surface geometry of exotic nuclei

    SciTech Connect

    Carlson, B. V.; Baldini-Neto, E.; Hirata, D.; Peru-Desenfants, S.; Berger, J.-F.; Chamon, L. C.

    2007-02-12

    We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data.

  7. Extending the ADM formalism to Weyl geometry

    SciTech Connect

    Barreto, A. B.; Almeida, T. S.; Romero, C.

    2015-03-26

    In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+l)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.

  8. Reactive-infiltration instability in radial geometry

    NASA Astrophysics Data System (ADS)

    Grodzki, Piotr; Szymczak, Piotr

    2015-04-01

    A planar dissolution front propagating through a homogeneous porous matrix is unstable with respect to small variations in local permeability; regions of high permeability dissolve faster because of enhanced transport of reactants, which leads to increased rippling of the front. This phenomenon, usually referred to known as reactive-infiltration instability is an important mechanism for pattern development in geology, with a range of morphologies and scales, from cave systems running for hundreds of miles to laboratory acidization on the scale of centimeters. In general, this instability is characterized by two length scales: the diffusive length (D/v) and the reactant penetration length (v/r), where v is the Darcy velocity, D - the diffusion constant and r - the dissolution rate. If the latter scale is much smaller than the former one can adopt the so-called thin front limit, where the interface is treated as a discontinuity in porosity, with a completely dissolved phase on one side and an undissolved phase on the other. Linear stability analysis for this case has been carried out by Chadam et al. [1], and the corresponding dispersion relation shows that long wavelengths are unstable, whereas short wavelengths are stabilized by diffusion. In their derivation, Chadam et al. have considered a linear geometry with a uniform pressure gradient applied along one of the directions. However, in many cases (e.g. in the acidization techniques used in oil industry) the reactive fluids are injected through a well and thus the relevant geometry is radial rather than linear. Motivated by this, we have carried out the linear stability analysis of the reactive-infiltration problem in radial geometry, with the fluid injection at the centre of the system. We stay within the thin-front limit and derive the corresponding dispersion relation, which shows the stable regions for both the long-wavelength and short-wavelength modes, and the unstable region in between. Next, we study how

  9. Programmable trap geometries with superconducting atom chips

    SciTech Connect

    Mueller, T.; Fermani, R.; Zhang, B.; Chan, K. S.; Dumke, R.; Lim, M. J.

    2010-05-15

    We employ the hysteretic behavior of a superconducting thin film in the remanent state to generate different traps and flexible magnetic potentials for ultracold atoms. The trap geometry can be programed by externally applied fields. This approach for atom optics is demonstrated by three different trap types realized on a single microstructure: a Z-type trap, a double trap, and a bias-field-free trap. Our studies show that superconductors in the remanent state provide a versatile platform for atom optics and applications in ultracold quantum gases.

  10. Joule heating in spin Hall geometry

    NASA Astrophysics Data System (ADS)

    Taniguchi, Tomohiro

    2016-07-01

    The theoretical formula for the entropy production rate in the presence of spin current is derived using the spin-dependent transport equation and thermodynamics. This theory is applicable regardless of the source of the spin current, for example, an electric field, a temperature gradient, or the Hall effect. It reproduces the result in a previous work on the dissipation formula when the relaxation time approximation is applied to the spin relaxation rate. By using the developed theory, it is found that the dissipation in the spin Hall geometry has a contribution proportional to the square of the spin Hall angle.

  11. Foucault pendulum and sub-Riemannian geometry

    NASA Astrophysics Data System (ADS)

    Anzaldo-Meneses, A.; Monroy-Pérez, F.

    2010-08-01

    The well known Foucault nonsymmetrical pendulum is studied as a problem of sub-Riemannian geometry on nilpotent Lie groups. It is shown that in a rotating frame a sub-Riemannian structure can be naturally introduced. For small oscillations, three dimensional horizontal trajectories are computed and displayed in detail. The fiber bundle structure is explicitly shown. The underlying Lie structure is described together with the corresponding holonomy group, which turns out to be given by the center of the Heisenberg group. Other related physical problems that can be treated in a similar way are also mentioned.

  12. Magnetic Resonance Spectra and Statistical Geometry.

    PubMed

    Earle, Keith A; Mainali, Laxman; Sahu, Indra Dev; Schneider, David J

    2010-01-01

    Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints which introduce curvature into parameter space and discuss the appropriate mathematical tools for treating curvature effects. Channel capacity, a term from communication theory, is suggested as a useful figure of merit for estimating the information content of spectra in the presence of noise. The tools introduced here are applied to the case of a model nitroxide system as a concrete example, but we stress that the methods described here are of general utility. PMID:20730032

  13. Phenomenology of effective geometries from quantum gravity

    NASA Astrophysics Data System (ADS)

    Torromé, Ricardo Gallego; Letizia, Marco; Liberati, Stefano

    2015-12-01

    In a recent paper [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015)] a general mechanism for the emergence of cosmological spacetime geometry from a quantum gravity setting was devised and a departure from standard dispersion relations for an elementary particle was predicted. We elaborate here on this approach extending the results obtained in that paper and showing that generically such a framework will not lead to higher order modified dispersion relations in the matter sector. Furthermore, we shall discuss possible phenomenological constraints to this scenario showing that spacetime will have to be classical to a very high degree by now in order to be consistent with current observations.

  14. Geometry program for aerodynamic lifting surface theory

    NASA Technical Reports Server (NTRS)

    Medan, R. T.

    1973-01-01

    A computer program that provides the geometry and boundary conditions appropriate for an analysis of a lifting, thin wing with control surfaces in linearized, subsonic, steady flow is presented. The kernel function method lifting surface theory is applied. The data which is generated by the program is stored on disk files or tapes for later use by programs which calculate an influence matrix, plot the wing planform, and evaluate the loads on the wing. In addition to processing data for subsequent use in a lifting surface analysis, the program is useful for computing area and mean geometric chords of the wing and control surfaces.

  15. Geometry in the large and hyperbolic chaos

    SciTech Connect

    Hasslacher, B.; Mainieri, R.

    1998-11-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.

  16. Massless Flavor in Geometry and Matrix Models

    SciTech Connect

    Roiban, Radu; Tatar, Radu; Walcher, Johannes

    2003-01-27

    The proper inclusion of flavor in the Dijkgraaf-Vafa proposal for the solution of N=1 gauge theories through matrix models has been subject of debate in the recent literature. We here reexamine this issue by geometrically engineering fundamental matter with type IIB branes wrapped on non-compact cycles in the resolved geometry, and following them through the geometric transition. Our approach treats massive and massless flavor fields on equal footing, including the mesons. We also study the geometric transitions and superpotentials for finite mass of the adjoint field. All superpotentials we compute reproduce the field theory results. Crucial insights come from T-dual brane constructions in type IIA.

  17. On the geometry of stiff knots

    NASA Astrophysics Data System (ADS)

    Pierre-Louis, O.

    2009-09-01

    We analyse the geometry of a thin knotted string with bending rigidity. Two types of geometric properties are investigated. First, following the approach of von der Mosel [H. von der Mosel, Asymptotic Anal. 18, 49 (1998)], we derive upper bounds for the multiplicity of crossings and braids. Then, using a general inequality for the length of 3D curves derived by Chakerian [G.D. Chakerian, Proc. of the American Math. Soc. 15, 886 (1964)], we analyze the size and confinement of a knot

  18. Twisted spectral geometry for the standard model

    NASA Astrophysics Data System (ADS)

    Martinetti, Pierre

    2015-07-01

    In noncommutative geometry, the spectral triple of a manifold does not generate bosonic fields, for fluctuations of the Dirac operator vanish. A Connes-Moscovici twist forces the commutative algebra to be multiplied by matrices. Keeping the space of spinors untouched, twisted-fluctuations then yield perturbations of the spin connection. Applied to the spectral triple of the Standard Model, a similar twist yields the scalar field needed to stabilize the vacuum and to make the computation of the Higgs mass compatible with its experimental value.

  19. Depth map generation from geometry and motion

    NASA Astrophysics Data System (ADS)

    Li, Qianmin; Ge, Chenyang; Ren, Pengju; Yao, Huimin

    2013-07-01

    As the demand for 3DTV keep increasing these years, the conversion from exist 2D videos to 3D ones becomes a new area of research. Depth map generation plays a key point in the process. Two most important clues of depth are geometry of the scene and motion vector. This paper presents an algorithm of depth map generation, which intends to get the depth map combines two aspects of information. Compared to the previous work, our method is improved in finding vanishing point, detect motion vectors, and depth map generation.

  20. The Local Geometry of Multiattribute Tradeoff Preferences.

    PubMed

    McGeachie, Michael; Doyle, Jon

    2011-05-01

    Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes. PMID:21528018

  1. Magnetic Resonance Spectra and Statistical Geometry

    PubMed Central

    Mainali, Laxman; Sahu, Indra Dev; Schneider, David J.

    2010-01-01

    Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints which introduce curvature into parameter space and discuss the appropriate mathematical tools for treating curvature effects. Channel capacity, a term from communication theory, is suggested as a useful figure of merit for estimating the information content of spectra in the presence of noise. The tools introduced here are applied to the case of a model nitroxide system as a concrete example, but we stress that the methods described here are of general utility. PMID:20730032

  2. Principal whitened gradient for information geometry.

    PubMed

    Yang, Zhirong; Laaksonen, Jorma

    2008-01-01

    We propose two strategies to improve the optimization in information geometry. First, a local Euclidean embedding is identified by whitening the tangent space, which leads to an additive parameter update sequence that approximates the geodesic flow to the optimal density model. Second, removal of the minor components of gradients enhances the estimation of the Fisher information matrix and reduces the computational cost. We also prove that dimensionality reduction is necessary for learning multidimensional linear transformations. The optimization based on the principal whitened gradients demonstrates faster and more robust convergence in simulations on unsupervised learning with synthetic data and on discriminant analysis of breast cancer data. PMID:18255260

  3. Information geometry of mean-field approximation.

    PubMed

    Tanaka, T

    2000-08-01

    I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics. PMID:10953246

  4. Information geometry of the spherical model.

    PubMed

    Janke, W; Johnston, D A; Kenna, R

    2003-04-01

    Motivated by the observation that geometrizing statistical mechanics offers an interesting alternative to more standard approaches, we calculate the scaling behavior of the curvature R of the information geometry metric for the spherical model. We find that R approximately epsilon(-2), where epsilon=beta(c)-beta is the distance from criticality. The discrepancy from the naively expected scaling R approximately epsilon(-3) is explained and compared with that for the Ising model on planar random graphs, which shares the same critical exponents. PMID:12786435

  5. Early Childhood Teacher Education: The Case of Geometry

    ERIC Educational Resources Information Center

    Clements, Douglas H.; Sarama, Julie

    2011-01-01

    For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and…

  6. Standard Definitions of Building Geometry for Energy Evaluation

    SciTech Connect

    Deru, M.; Torcellini, P.

    2005-10-01

    This document provides definitions and metrics of building geometry for use in building energy evaluation. Building geometry is an important input in the analysis process, yet there are no agreed-upon standard definitions of these terms for use in energy analysis. The metrics can be used for characterizing building geometry, for calculating energy performance metrics, and for conducting energy simulations.

  7. Developing the Concept of a Parabola in Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba; Kurtulus, Aytaç; Yanik, H. Bahadir

    2015-01-01

    The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student.…

  8. Problem Solving in Calculus with Symbolic Geometry and CAS

    ERIC Educational Resources Information Center

    Todd, Philip; Wiechmann, James

    2008-01-01

    Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

  9. A Brief History of Non-Euclidean Geometry

    ERIC Educational Resources Information Center

    Marshall, Daniel; Scott, Paul

    2004-01-01

    Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

  10. Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry

    ERIC Educational Resources Information Center

    Guven, Bulent; Baki, Adnan

    2010-01-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

  11. An Alternative Approach to Logo-Based Geometry

    ERIC Educational Resources Information Center

    Durmus, Soner; Karakirik, Erol

    2005-01-01

    Geometry is an important branch of mathematics. Geometry curriculum can be enriched by using different Technologies such as graphing calculators and computers. Logo-based different software packages aim to improve conceptual understanding in geometry. The goals of this paper are i) to present theoretical foundations of any computer software…

  12. An Alternative Approach to Logo-Based Geometry

    ERIC Educational Resources Information Center

    Karakirik, Erol; Durmus, Soner

    2005-01-01

    Geometry is an important branch of mathematics. Geometry curriculum can be enriched by using different Technologies such as graphing calculators and computers. Logo-based different software packages aim to improve conceptual understanding in geometry. The goals of this paper are i) to present theoretical foundations of any compute software…

  13. Multigroup Complex Geometry Neutron Diffusion Code System.

    Energy Science and Technology Software Center (ESTSC)

    2002-12-18

    Version 01 SNAP-3D is based on SNAP2 and is a one- two- or three-dimensional multigroup diffusion code system. It is primarily intended for neutron diffusion calculations, but it can also carry out gamma-ray calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP-3D can solve the multi-group neutron diffusion equations using finite difference methods in (x,y,z), (r,theta,z), (TRI,z), (HEX,z) or (spherical) coordinates.more » The one-dimensional slab and cylindrical geometries and the two-dimensional (x,y), (r,z), (r,theta), (HEX) and (TRI) are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. The problem classes are: 1) eigenvalue search for critical k-effective, 2) eigenvalue search for critical buckling, 3) eigenvalue search for critical time-constant, 4) fixed source problems in which the sources are functions of regions, 5) fixed source problems in which the sources are provided, on disc, for every mesh point and group.« less

  14. Conical Rotating Aperture Geometries In Digital Radiography

    NASA Astrophysics Data System (ADS)

    Rudin, Stephen; Bednarek, Daniel R.; Wong, Roland

    1981-11-01

    Applications of conical rotating aperture (RA) geometries to digital radiography are described. Two kinds of conical RA imaging systems are the conical scanning beam and the conical scanning grid assemblies. These assemblies comprise coaxial conical surface(s) the axis of which is collinear with the x-ray focal spot. This geometry allows accurate alignment and continuous focusing of the slits or the grid lines. Image receptors which use solid state photodiode arrays are described for each type of conical RA system: multiple linear arrays for the conical scanning beam assembly and multiple area arrays for the conical scanning grid assembly. The digital rotating-aperture systems combine the wide dynamic range characteristics of solid state detectors with the superior scatter-rejection advantages of scanned beam approaches. The high scanning-beam velocities attainable by the use of rotating apertures should make it possible to obtain digital images for those procedures such as chest radiography which require large fields of view and short exposure times.

  15. Pulsar Emission Geometry and Accelerating Field Strength

    NASA Technical Reports Server (NTRS)

    DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien

    2012-01-01

    The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry

  16. Probing the geometry of the Laughlin state

    DOE PAGESBeta

    Johri, Sonika; Papic, Z.; Schmitteckert, P.; Bhatt, R. N.; Haldane, F. D. M.

    2016-02-05

    It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantumHall states—the filling v = 1/3 Laughlin state.We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulkmore » off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a ‘pair amplitude’ operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. Furthermore, these various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.« less

  17. Study on Pyroelectric Harvesters with Various Geometry

    PubMed Central

    Siao, An-Shen; Chao, Ching-Kong; Hsiao, Chun-Ching

    2015-01-01

    Pyroelectric harvesters convert time-dependent temperature variations into electric current. The appropriate geometry of the pyroelectric cells, coupled with the optimal period of temperature fluctuations, is key to driving the optimal load resistance, which enhances the performance of pyroelectric harvesters. The induced charge increases when the thickness of the pyroelectric cells decreases. Moreover, the induced charge is extremely reduced for the thinner pyroelectric cell when not used for the optimal period. The maximum harvested power is achieved when a 100 μm-thick PZT (Lead zirconate titanate) cell is used to drive the optimal load resistance of about 40 MΩ. Moreover, the harvested power is greatly reduced when the working resistance diverges even slightly from the optimal load resistance. The stored voltage generated from the 75 μm-thick PZT cell is less than that from the 400 μm-thick PZT cell for a period longer than 64 s. Although the thinner PZT cell is advantageous in that it enhances the efficiency of the pyroelectric harvester, the much thinner 75 μm-thick PZT cell and the divergence from the optimal period further diminish the performance of the pyroelectric cell. Therefore, the designers of pyroelectric harvesters need to consider the coupling effect between the geometry of the pyroelectric cells and the optimal period of temperature fluctuations to drive the optimal load resistance. PMID:26270666

  18. Study on Pyroelectric Harvesters with Various Geometry.

    PubMed

    Siao, An-Shen; Chao, Ching-Kong; Hsiao, Chun-Ching

    2015-01-01

    Pyroelectric harvesters convert time-dependent temperature variations into electric current. The appropriate geometry of the pyroelectric cells, coupled with the optimal period of temperature fluctuations, is key to driving the optimal load resistance, which enhances the performance of pyroelectric harvesters. The induced charge increases when the thickness of the pyroelectric cells decreases. Moreover, the induced charge is extremely reduced for the thinner pyroelectric cell when not used for the optimal period. The maximum harvested power is achieved when a 100 μm-thick PZT (Lead zirconate titanate) cell is used to drive the optimal load resistance of about 40 MΩ. Moreover, the harvested power is greatly reduced when the working resistance diverges even slightly from the optimal load resistance. The stored voltage generated from the 75 μm-thick PZT cell is less than that from the 400 μm-thick PZT cell for a period longer than 64 s. Although the thinner PZT cell is advantageous in that it enhances the efficiency of the pyroelectric harvester, the much thinner 75 μm-thick PZT cell and the divergence from the optimal period further diminish the performance of the pyroelectric cell. Therefore, the designers of pyroelectric harvesters need to consider the coupling effect between the geometry of the pyroelectric cells and the optimal period of temperature fluctuations to drive the optimal load resistance. PMID:26270666

  19. Measurement of quantum fluctuations in geometry

    NASA Astrophysics Data System (ADS)

    Hogan, Craig J.

    2008-05-01

    A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the context of a holographic geometry with a minimum length at the Planck scale. The indeterminacy predicts fluctuations from a classically defined geometry in the form of “holographic noise” whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometric gravitational-wave detector GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as the LIGO observatories, where beam power is much less in the beam splitter than in the arms.

  20. Quantitative analysis of blood vessel geometry

    NASA Astrophysics Data System (ADS)

    Fuhrman, Michael G.; Abdul-Karim, Othman; Shah, Sujal; Gilbert, Steven G.; Van Bibber, Richard

    2001-07-01

    Re-narrowing or restenosis of a human coronary artery occurs within six months in one third of balloon angioplasty procedures. Accurate and repeatable quantitative analysis of vessel shape is important to characterize the progression and type of restenosis, and to evaluate effects new therapies might have. A combination of complicated geometry and image variability, and the need for high resolution and large image size makes visual/manual analysis slow, difficult, and prone to error. The image processing and analysis described here was developed to automate feature extraction of the lumen, internal elastic lamina, neointima, external elastic lamina, and tunica adventitia and to enable an objective, quantitative definition of blood vessel geometry. The quantitative geometrical analysis enables the measurement of several features including perimeter, area, and other metrics of vessel damage. Automation of feature extraction creates a high throughput capability that enables analysis of serial sections for more accurate measurement of restenosis dimensions. Measurement results are input into a relational database where they can be statistically analyzed compared across studies. As part of the integrated process, results are also imprinted on the images themselves to facilitate auditing of the results. The analysis is fast, repeatable and accurate while allowing the pathologist to control the measurement process.

  1. Dimensional flow in discrete quantum geometries

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2015-04-01

    In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0 <α geometries may be considered as fractal only when α =1 , where the "magic number" DS≃2 for the spectral dimension of spacetime, appearing so often in quantum gravity, is reproduced as well. These results apply, in particular, to special superpositions of spin-network states in loop quantum gravity, and they provide more solid indications of dimensional flow in this approach.

  2. Lobed Mixer Optimization for Advanced Ejector Geometries

    NASA Technical Reports Server (NTRS)

    Waitz, Ian A.

    1996-01-01

    The overall objectives are: 1) to pursue analytical, computational, and experimental studies that enhance basic understanding of forced mixing phenomena relevant to supersonic jet noise reduction, and 2) to integrate this enhanced understanding (analytical, computational, and empirical) into a design-oriented model of a mixer-ejector noise suppression system. The work is focused on ejector geometries and flow conditions typical of those being investigated in the NASA High Speed Research Program (HSRP). The research will be carried out in collaboration with the NASA HSRP Nozzle Integrated Technology Development (ITD) Team, and will both contribute to, and benefit from, the results of other HSRP research. The noise suppressor system model that is being developed under this grant is distinct from analytical tools developed by industry because it directly links details of lobe geometry to mixer-ejector performance. In addition, the model provides a 'technology road map to define gaps in the current understanding of various phenomena related to mixer-ejector design and to help prioritize research areas. This report describes research completed in the past year, as well as work proposed for the following year.

  3. Magnetic geometry, plasma profiles, and stability

    SciTech Connect

    Connor, J. W.

    2006-07-15

    The history of the stability of short wavelength modes, such as MHD instabilities and drift waves, has been a long and tortuous one as increasingly realistic representations of the equilibrium magnetic geometry have been introduced. Early work began with simple slab or cylindrical models where plasma profiles and magnetic shear were seen to play key roles. Then the effects of toroidal geometry, in particular the constraints imposed by periodicity in the presence of magnetic shear, provided a challenge for theory, which was met by the ballooning transformation. More recently the limitations on the conventional ballooning theory arising from effects such as toroidal rotation shear, low magnetic shear, and the presence of the plasma edge have been recognized. These have led in turn to modifications and extensions of this theory. These developments have produced a continuously changing view of the stability of the 'universal' drift wave, for example. After a survey of this background, we describe more recent work of relevance to currently important topics, such as transport barriers characterized by the presence of strong rotation shear and low magnetic shear and the edge localized modes that occur in H-mode.

  4. Time, temperature, and data cloud geometry.

    PubMed

    Fushing, Hsieh; McAssey, Michael P

    2010-12-01

    We demonstrate that the geometry of a data cloud is computable on multiple scales without prior knowledge about its structure. We show that the concepts of "time" and "temperature" are beneficial for constructing a hierarchical geometry based on local information provided by a similarity measure. We design two devices for construction of this hierarchy. Along the time axis, a regulated random walk incorporated with recurrence-time dynamics detects information about the number of clusters and the corresponding cluster membership of individual data nodes. Along the temperature axis we build the geometric hierarchy of a data cloud, which consists of only a few phase transitions. The base level of the hierarchy especially exhibits the intrinsic data structure. At each chosen temperature, we form an ensemble matrix that summarizes information extracted from many regulated random walks. This device constitutes the basis for constructing one corresponding level of the hierarchy by means of spectral clustering. We illustrate the construction of such geometric hierarchies using simulated and real data. PMID:21230647

  5. Geometry as an aspect of dynamics

    NASA Astrophysics Data System (ADS)

    Videira, A. L. L.; Barros, A. L. Rocha; Fernandes, N. C.

    1985-12-01

    Contrary to the predominant way of doing physics, we claim that the geometrical structure of a general differentiable space-time manifold can be determined from purely dynamical considerations. Any n-dimensional manifold V a has associated with it a symplectic structure given by the 2n numbers p and x of the 2n-dimensional cotangent fiber bundle TVn. Hence, one is led, in a natural way, to the Hamiltonian description of dynamics, constructed in terms of the covariant momentum p (a dynamical quantity) and of the contravariant position vector x (a geometrical quantity). That is, the Hamiltonian description furnishes a natural way of relating dynamics and geometry. Thus, starting from the Hamiltonian state function (for a particle)—taken as the fundamental dynamical entity—we show that general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and nonrelativistic dynamics is bound up to Newton-Cartan space-time.

  6. TES Limb-Geometry Observations of Aerosols

    NASA Technical Reports Server (NTRS)

    Smith, Michael D.

    2003-01-01

    The Thermal Emission Spectrometer (TES) on-board Mars Global Surveyor (MGS) has a pointing mirror that allows observations in the plane of the orbit anywhere from directly nadir to far above either the forward or aft limbs for details about the TES instrument). Nadir-geometry observations are defined as those where the field-of-view contains the surface of Mars (even if the actual observation is at a high emission angle far from true nadir). Limb-geometry observations are defined as those where the line-of-sight of the observations does not intersect the surface. At a number of points along the MGS orbit (typically every 10 deg. or 20 deg. of latitude) a limb sequence is taken, which includes a stack of overlapping TES spectra from just below the limb to more than 120 km above the limb. A typical limb sequence has approx. 20 individual spectra, and the projected size of a TES pixel at the limb is 13 km.

  7. A method of plane geometry primitive presentation

    NASA Astrophysics Data System (ADS)

    Jiao, Anbo; Luo, Haibo; Chang, Zheng; Hui, Bin

    2014-11-01

    Point feature and line feature are basic elements in object feature sets, and they play an important role in object matching and recognition. On one hand, point feature is sensitive to noise; on the other hand, there are usually a huge number of point features in an image, which makes it complex for matching. Line feature includes straight line segment and curve. One difficulty in straight line segment matching is the uncertainty of endpoint location, the other is straight line segment fracture problem or short straight line segments joined to form long straight line segment. While for the curve, in addition to the above problems, there is another difficulty in how to quantitatively describe the shape difference between curves. Due to the problems of point feature and line feature, the robustness and accuracy of target description will be affected; in this case, a method of plane geometry primitive presentation is proposed to describe the significant structure of an object. Firstly, two types of primitives are constructed, they are intersecting line primitive and blob primitive. Secondly, a line segment detector (LSD) is applied to detect line segment, and then intersecting line primitive is extracted. Finally, robustness and accuracy of the plane geometry primitive presentation method is studied. This method has a good ability to obtain structural information of the object, even if there is rotation or scale change of the object in the image. Experimental results verify the robustness and accuracy of this method.

  8. Thermoacoustic engines in alternate geometry resonators

    NASA Astrophysics Data System (ADS)

    Lightfoot, Jay Alan

    1997-10-01

    The purpose of this research is to branch out from thermoacoustics in the plane wave geometry to study radial wave thermoacoustic engines. Two possible advantages of radial systems are proposed: a reduction in harmonic generation due to the natural anharmonicity of the resonator, and the possibility of improved engine performance using naturally sloped stacks. The radial wave prime mover is described. Experimental results for the temperature at which oscillations begin are compared with theoretical predictions. Accounting for a pore distribution in the stack and temperature discontinuities between the stack and heat exchangers, theory and experiment are shown to be in agreement. In addition, spectral measurements in the radial prime mover show that the anharmonicity of the resonator significantly reduces non-linear harmonic generation. To gain a better understanding of naturally sloped stacks in the radial engine, the physics of sloped stacks is extended to the plane geometry, where fewer constraints exist. A theoretical treatment of thermoacoustic engines with varying stack pore cross-section and/or varying resonator cross-section in the temperature gradient supporting stack region is presented along with numerical results for plane and radial wave prime movers and refrigerators. Results show significant improvements in refrigerator COP in plane wave systems.

  9. Geometry and self-righting of turtles

    PubMed Central

    Domokos, Gábor; Várkonyi, Péter L

    2007-01-01

    Terrestrial animals with rigid shells face imminent danger when turned upside down. A rich variety of righting strategies of beetle and turtle species have been described, but the exact role of the shell's geometry in righting is so far unknown. These strategies are often based on active mechanisms, e.g. most beetles self-right via motion of their legs or wings; flat, aquatic turtles use their muscular neck to flip back. On the other hand, highly domed, terrestrial turtles with short limbs and necks have virtually no active control: here shape itself may serve as a fundamental tool. Based on field data gathered on a broad spectrum of aquatic and terrestrial turtle species we develop a geometric model of the shell. Inspired by recent mathematical results, we demonstrate that a simple mechanical classification of the model is closely linked to the animals' righting strategy. Specifically, we show that the exact geometry of highly domed terrestrial species is close to optimal for self-righting, and the shell's shape is the predominant factor of their ability to flip back. Our study illustrates how evolution solved a far-from-trivial geometrical problem and equipped some turtles with monostatic shells: beautiful forms, which rarely appear in nature otherwise. PMID:17939984

  10. Variable geometry device for turbine compressor outlet

    NASA Technical Reports Server (NTRS)

    Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)

    1985-01-01

    A variable geometry device is provided for use with the compressor outlet of a turbine engine. The turbine engine includes a support housing, a compressor contained within the support housing and having a compressed air outlet and in which a pair of spaced walls define an annular and radially extending diffuser passageway. The inner end of the diffuser passageway is open to the compressed outlet while the outer end of the diffuser passageway is open to the combustion chamber for the turbine engine. A plurality of circumferentially spaced diffuser vanes are mounted to one of the diffuser walls and protrude across the diffuser passageway. An annular recessed channel is formed around the opposite diffuser wall and an annular ring is mounted within the channel. A motor is operatively connected to this ring and, upon actuation, displaces the ring transversely across the diffuser passageway to variably restrict the diffuser passageway. In addition, the ring includes a plurality of slots which register with the diffuser vanes so that the vane geometry remains the same despite axial displacement of the ring.

  11. Students' Learning Experiences When Using a Dynamic Geometry Software Tool in a Geometry Lesson at Secondary School in Ethiopia

    ERIC Educational Resources Information Center

    Denbel, Dejene Girma

    2015-01-01

    Students learning experiences were investigated in geometry lesson when using Dynamic Geometry Software (DGS) tool in geometry learning in 25 Ethiopian secondary students. The research data were drawn from the used worksheets, classroom observations, results of pre- and post-test, a questionnaire and interview responses. I used GeoGebra as a DGS…

  12. The relationship among geometry, working memory, and intelligence in children.

    PubMed

    Giofrè, David; Mammarella, Irene Cristina; Cornoldi, Cesare

    2014-07-01

    Although geometry is one of the main areas of mathematical learning, the cognitive processes underlying geometry-related academic achievement have not been studied in detail. This study explored the relationship among working memory (WM), intelligence (g factor), and geometry in 176 typically developing children attending school in their fourth and fifth grades. Structural equation modeling showed that approximately 40% of the variance in academic achievement and in intuitive geometry (which is assumed to be independent of a person's cultural background) was explained by WM and the g factor. After taking intelligence and WM into account, intuitive geometry was no longer significantly related to academic achievement in geometry. We also found intuitive geometry to be closely related to fluid intelligence (as measured by Raven's colored progressive matrices) and reasoning ability, whereas academic achievement in geometry depended largely on WM. These results were confirmed by a series of regressions in which we estimated the contributions of WM, intelligence, and intuitive geometry to the unique and shared variance explaining academic achievement in geometry. Theoretical and educational implications of the relationship among WM, intelligence, and academic achievement in geometry are discussed. PMID:24709286

  13. Improving Seismic Constraints on Subduction Zone Geometry

    NASA Astrophysics Data System (ADS)

    Syracuse, E. M.; Abers, G. A.; Fischer, K. M.; van Keken, P. E.; Kneller, E. A.; Rychert, C. A.

    2007-12-01

    Accurate slab geometries are necessary for 3D flow modeling, and for understanding the variations in temperature and melting geometry between different subduction zones. Recent studies have shown that the depth to slab beneath arc volcanoes varies by as much as a factor of two between subduction zones, but these results are based on teleseismic earthquake catalogs with potentially large errors. When available, local seismic arrays provide better constraints. The TUCAN array (Tomography Under Costa Rica and Nicaragua) deployed 48 three component broadband PASSCAL instruments for 18 months with station spacing of 10-50 km across the Central America arc. This dataset provides some of the best control anywhere for ground-truth comparison of teleseismic catalogs in steeply dipping subduction zones. Joint inversion of TUCAN arrival times for velocity and hypocenters illuminate a 10-15 km thick Wadati-Benioff zone (WBZ), with absolute hypocenter uncertainties of 1-5 km. Besides providing accurate hypocenters, the tomographic images provide independent constraints on melting and temperature, through the imaging of low Vp (7.5-7.8 km/s) and highly attenuating (40

  14. Interferometric tests of Planckian quantum geometry models

    NASA Astrophysics Data System (ADS)

    Kwon, Ohkyung; Hogan, Craig J.

    2016-05-01

    The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for nonstandard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographic bounds on directional information. Predictions in this case are shown to be close to current and projected experimental bounds.

  15. Scalar waves in a wormhole geometry

    SciTech Connect

    Kar, S.; Sahdev, D. ); Bhawal, B. )

    1994-01-15

    The reflection and transmission of massless scalar waves in the curved background geometry of a typical Lorentzian wormhole (in 2+1 and 3+1 dimensions) are discussed. Using the exact solutions which involve modified Mathieu (in 2+1 dimensions) and radial oblate spheroidal (in 3+1 dimensions) functions, explicit analytic expressions are obtained for the reflection and transmission coefficients at specific values of the quantity [omega][ital b][sub 0] ([omega] being the energy of the scalar wave and [ital b][sub 0] the throat radius of the wormhole). It is found that both near-perfect reflection as well as transmission are possible for specific choices of certain parameters.

  16. Gully geometry: what are we measuring?

    NASA Astrophysics Data System (ADS)

    Casalí, Javier; Giménez, Rafael; Ángel Campo, Miguel

    2014-05-01

    Gully erosion has attracted the attention of many scientists during the last decades, and gullies are an important source of sediment within catchments. For succeeding in gully erosion research, gullies must be properly characterized. Characterization includes the determination of gully morphology and volume, being the definition of gully width (W) and depth (D) -and consequently related variables such as the well-known W/D ratio- key issues toward to this goal. However, and surprisingly, universally accepted criteria (rules or guidance) to define gully morphology are lacking. This because the protocol every researcher follows to measure the eroded channel geometry is generally taken for granted and most of the time even no explanation is given about it. For example, when analyzing a gully cross section we usually just identify gully depth with gully maximum depth. But, is this the right protocol? What does this length really represent? What is its meaning? All this uncertainties can lead to non-comparable results and then important inconsistencies. So, to define universal rules of procedure would allow gully scientists "speak the same language" and then deliver truly comparable gully geometry and volume. On the other hand, there are other misunderstandings. For example, very frequently we characterize or depict a whole gully only through some of its cross sections. Again, is this correct? The problem is even more complex when considering that gully geometry may (largely) change along the channel. The main aim of this presentation is to highlight some (unnoticed) common flaws when measuring and describing gully geometry, hoping ultimately to open a debate on that subject. For this last purpose, a conceptual approach to define gully cross section width and other derived variables is firstly proposed. It is based on the subtraction of a highly detailed digital elevation model of a landscape surface containing the studied gully (DEM1) from a detailed spatial

  17. Exotic geometry in string theory and cosmology

    NASA Astrophysics Data System (ADS)

    Haque, Sheikh Shajid

    One of the main features expected of a quantum theory of gravity is non-locality. Implementing non-locality in quantum field theories turns out to be already challenging both conceptually and technically and requires the use of several techniques, such as string dualities and twists in order to construct and understand the effects of non-locality. This thesis explored these concepts in the construction of quantum field theories with a particular type of non- locality, non-commutative geometry, as an opportunity to study non-locality in a broader context. Another important challenge of theoretical physics is to connect the microscopic structure of spacetime implied by string theory to the empirical fact that the cosmological constant is positive and that the universe is asymptotically de Sitter. Constructing de Sitter space from string theory has proven to be extremely difficult over the years. In this thesis, I will discuss recent work in these areas.

  18. Graded geometry in gauge theories and beyond

    NASA Astrophysics Data System (ADS)

    Salnikov, Vladimir

    2015-01-01

    We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using this concept we describe a procedure for analysis of gauge symmetries of given functionals as well as for constructing functionals (sigma models) invariant under an action of some gauge group. As the main example of application of these constructions we consider the twisted Poisson sigma model. We obtain it by a gauging-type procedure of the action of an essentially infinite dimensional group and describe its symmetries in terms of classical differential geometry. We comment on other possible applications of the described concept including the analysis of supersymmetric gauge theories and higher structures.

  19. BRST, anti-BRST and their geometry

    NASA Astrophysics Data System (ADS)

    Bonora, L.; Malik, R. P.

    2010-09-01

    We continue the comparison between the field theoretical and geometrical approaches to the gauge field theories of various types, by deriving their Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST transformation properties and comparing them with the geometrical properties of the bundles and gerbes. In particular, we provide the geometrical interpretation of the so-called Curci-Ferrari conditions that are invoked for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations in the context of non-Abelian one-form gauge theories as well as the Abelian gauge theory that incorporates a two-form gauge field. We also carry out the explicit construction of the three-form gauge fields and compare it with the geometry of 2-gerbes.

  20. Deception discovery and employment with linguistic geometry

    NASA Astrophysics Data System (ADS)

    Stilman, Boris; Yakhnis, Vladimir; Curry, Pat; Umanskiy, Oleg

    2005-05-01

    No battle plan survives first contact with the enemy - this is a famous adage attributed to a great many military thinkers from Belisarius to Clausewitz, but which is essentially timeless. Indeed, while the Blue side is trying to anticipate and predict the enemy action, this enemy is actively trying to do the same with respect to Blue while simultaneously trying to deny Blue sufficient information on which to predict Red's actions. It becomes even worse when the Red side is actively engaged in deceptive behavior leading to ambushes and other deceptive schemes causing losses to the Blue side. Linguistic Geometry (LG), a new game-theoretical approach, permits uncovering enemy deceptive schemes via indicators and probes. We will describe the theory behind the LG approach to deception and discuss a specific example of discerning enemy deception via LG algorithms.

  1. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  2. BOREAS TE-12 SSA Shoot Geometry Data

    NASA Technical Reports Server (NTRS)

    Hall, Forrest G. (Editor); Curd, Shelaine (Editor); Walter-Shea, Elizabeth A.; Mesarch, Mark A.; Cheng, L.; Yang, Litao

    2000-01-01

    The Boreal Ecosystem-Atmospheric Study (BOREAS) TE-12 (Terrestrial Ecology) team collected shoot geometry data in 1993 and 1994 from aspen, jack pine, and black spruce trees. Collections were made at the Southern Study Area Nipawin Fen Site (SSA FEN), Young Jack Pine (YJP), Old Jack Pine (OJP), Old Aspen (OA), Young Aspen (YA), Mixed Site (MIX), and Old Black Spruce (OBS) sites. A caliper was used to measure shoot and needle lengths and widths. A volume displacement procedure was used to measure the weight of the shoot or twig submerged in water. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

  3. Algebraic geometry realization of quantum Hall soliton

    NASA Astrophysics Data System (ADS)

    Abounasr, R.; Ait Ben Haddou, M.; El Rhalami, A.; Saidi, E. H.

    2005-02-01

    Using the Iqbal-Netzike-Vafa dictionary giving the correspondence between the H2 homology of del Pezzo surfaces and p-branes, we develop a way to approach the system of brane bounds in M-theory on S1. We first review the structure of 10-dimensional quantum Hall soliton (QHS) from the view of M-theory on S1. Then, we show how the D0 dissolution in D2-brane is realized in M-theory language and derive the p-brane constraint equations used to define appropriately the QHS. Finally, we build an algebraic geometry realization of the QHS in type IIA superstring and show how to get its type IIB dual. Other aspects are also discussed.

  4. The Bell states in noncommutative algebraic geometry

    NASA Astrophysics Data System (ADS)

    Beil, Charlie

    2014-10-01

    We introduce new mathematical aspects of the Bell states using matrix factorizations, non-noetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial p consists of two matrices ϕ1, ϕ2 such that ϕ1ϕ2 = ϕ2ϕ1 = p id. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on non-noetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.

  5. Interactive design of hypersonic waverider geometries

    NASA Technical Reports Server (NTRS)

    Center, K. B.; Sobieczky, H.; Dougherty, F. C.

    1991-01-01

    The paper deals with an inverse design code utilizing the method of oscillating cones; the code integrated into an interactive graphics software package allows manipulation of both the exit-plane shock profile and leading edge of the vehicle. Another interactive feature of the system is the ability to vary freestream conditions and reevaluate the governing conditions. The development of the oscillating cones is shown on five classes each of which is chosen to demonstrate an aspect of improved design flexibility over previous studies. Results are evaluated using a robust flow solver, insuring that the shock shapes specified in the design process are recovered. It is pointed out that the expanded range of waverider geometries that may be generated using the oscillating cones technique may provide insight into visually oriented optimization parameters such as volumetric efficiency and practical planform.

  6. Geometry of aortic heart valves. [prosthetic design

    NASA Technical Reports Server (NTRS)

    Karara, H. M.

    1975-01-01

    Photogrammetric measurements of the surface topography of the aortic valves obtained from silicon rubber molds of freshly excised human aortic valves are presented. The data are part of an investigation into the design of a new prosthetic valve which will be a central-flow device, like the real valve and unlike previous central-occluding prostheses. Since the maximum stress on the heart valve is induced when the valve is closed and subject to diastolic back-pressure, it was decided to determine the valve geometry during diastole. That is, the molds were formed by pouring the rubber down the excised aortas, causing the valves to close. The molds were made under different pressures (20-120 torr); photogrammetry served as a vehicle for the assessment of the mold topography through the following outputs: digital models, surface profiles, and contour maps.

  7. Black holes and large order quantum geometry

    SciTech Connect

    Huang Minxin; Klemm, Albrecht; Marino, Marcos; Tavanfar, Alireza

    2009-03-15

    We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations--which seem necessary to resolve the so-called entropy enigma in the Ooguri-Strominger-Vafa conjecture--do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.

  8. Geometry and mechanics of thin growing bilayers.

    PubMed

    Pezzulla, Matteo; Smith, Gabriel P; Nardinocchi, Paola; Holmes, Douglas P

    2016-05-11

    We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourths the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. PMID:27098344

  9. Geometry and Mechanics of Thin Growing Bilayers

    NASA Astrophysics Data System (ADS)

    Pezzulla, Matteo; Smith, Gabriel; Nardinocchi, Paola; Holmes, Douglas

    We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourth's the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. NSF Grant CMMI-1300860.

  10. Gap geometry dictates epithelial closure efficiency

    PubMed Central

    Ravasio, Andrea; Cheddadi, Ibrahim; Chen, Tianchi; Pereira, Telmo; Ong, Hui Ting; Bertocchi, Cristina; Brugues, Agusti; Jacinto, Antonio; Kabla, Alexandre J.; Toyama, Yusuke; Trepat, Xavier; Gov, Nir; Neves de Almeida, Luís; Ladoux, Benoit

    2015-01-01

    Closure of wounds and gaps in tissues is fundamental for the correct development and physiology of multicellular organisms and, when misregulated, may lead to inflammation and tumorigenesis. To re-establish tissue integrity, epithelial cells exhibit coordinated motion into the void by active crawling on the substrate and by constricting a supracellular actomyosin cable. Coexistence of these two mechanisms strongly depends on the environment. However, the nature of their coupling remains elusive because of the complexity of the overall process. Here we demonstrate that epithelial gap geometry in both in vitro and in vivo regulates these collective mechanisms. In addition, the mechanical coupling between actomyosin cable contraction and cell crawling acts as a large-scale regulator to control the dynamics of gap closure. Finally, our computational modelling clarifies the respective roles of the two mechanisms during this process, providing a robust and universal mechanism to explain how epithelial tissues restore their integrity. PMID:26158873

  11. Simulating Irregular Source Geometries for Ionian Plumes

    SciTech Connect

    McDoniel, W. J.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Buchta, D. A.; Freund, J.; Kieffer, S. W.

    2011-05-20

    Volcanic plumes on Io respresent a complex rarefied flow into a near-vacuum in the presence of gravity. A 3D Direct Simulation Monte Carlo (DSMC) method is used to investigate the gas dynamics of such plumes, with a focus on the effects of source geometry on far-field deposition patterns. A rectangular slit and a semicircular half annulus are simulated to illustrate general principles, especially the effects of vent curvature on deposition ring structure. Then two possible models for the giant plume Pele are presented. One is a curved line source corresponding to an IR image of a particularly hot region in the volcano's caldera and the other is a large area source corresponding to the entire caldera. The former is seen to produce the features seen in observations of Pele's ring, but with an error in orientation. The latter corrects the error in orientation, but loses some structure. A hybrid simulation of 3D slit flow is also discussed.

  12. Consciousness, the brain, and spacetime geometry.

    PubMed

    Hameroff, S

    2001-04-01

    subunit proteins ("tubulins") within certain brain neurons, remain coherent, and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached. At that point, self-collapse, or objective reduction (OR), abruptly occurs. We equate the pre-reduction, coherent superposition ("quantum computing") phase with pre-conscious processes, and each instantaneous (and non-computable) OR, or self-collapse, with a discrete conscious event. Sequences of OR events give rise to a "stream" of consciousness. Microtubule-associated proteins can "tune" the quantum oscillations of the coherent superposed states; the OR is thus self-organized, or "orchestrated" ("Orch OR"). Each Orch OR event selects (non-computably) microtubule subunit states which regulate synaptic/neural functions using classical signaling. The quantum gravity threshold for self-collapse is relevant to consciousness, according to our arguments, because macroscopic superposed quantum states each have their own spacetime geometries. These geometries are also superposed, and in some way "separated," but when sufficiently separated, the superposition of spacetime geometries becomes significantly unstable and reduces to a single universe state. Quantum gravity determines the limits of the instability; we contend that the actual choice of state made by Nature is non-computable. Thus each Orch OR event is a self-selection of spacetime geometry, coupled to the brain through microtubules and other biomolecules. If conscious experience is intimately connected with the very physics underlying spacetime structure, then Orch OR in microtubules indeed provides us with a completely new and uniquely promising perspective on the difficult problems of consciousness. PMID:11349432

  13. From natural geometry to spatial cognition.

    PubMed

    Tommasi, Luca; Chiandetti, Cinzia; Pecchia, Tommaso; Sovrano, Valeria Anna; Vallortigara, Giorgio

    2012-02-01

    A review of selected works on spatial memory in animals and humans is presented, and some ideas about the encoding of geometry and its role in evolution are presented, based on recently accumulated evidence from psychology, ethology and the neurosciences. It is argued that comparative analyses at the level of both spatial navigation behaviors and their underlying neural mechanisms may provide a solid foundation for the biological origins of organisms' spontaneous ability in dealing with geometric concepts. To this aim, the representations of space underlying memory tasks involving discrete (i.e., landmark arrays) or continuous elements (i.e., enclosed environments) are evaluated and compared as regards the impact of their geometric arrangement. PMID:22206900

  14. Gap geometry dictates epithelial closure efficiency.

    PubMed

    Ravasio, Andrea; Cheddadi, Ibrahim; Chen, Tianchi; Pereira, Telmo; Ong, Hui Ting; Bertocchi, Cristina; Brugues, Agusti; Jacinto, Antonio; Kabla, Alexandre J; Toyama, Yusuke; Trepat, Xavier; Gov, Nir; Neves de Almeida, Luís; Ladoux, Benoit

    2015-01-01

    Closure of wounds and gaps in tissues is fundamental for the correct development and physiology of multicellular organisms and, when misregulated, may lead to inflammation and tumorigenesis. To re-establish tissue integrity, epithelial cells exhibit coordinated motion into the void by active crawling on the substrate and by constricting a supracellular actomyosin cable. Coexistence of these two mechanisms strongly depends on the environment. However, the nature of their coupling remains elusive because of the complexity of the overall process. Here we demonstrate that epithelial gap geometry in both in vitro and in vivo regulates these collective mechanisms. In addition, the mechanical coupling between actomyosin cable contraction and cell crawling acts as a large-scale regulator to control the dynamics of gap closure. Finally, our computational modelling clarifies the respective roles of the two mechanisms during this process, providing a robust and universal mechanism to explain how epithelial tissues restore their integrity. PMID:26158873

  15. New irradiation geometry for microbeam radiation therapy

    NASA Astrophysics Data System (ADS)

    Bräuer-Krisch, E.; Requardt, H.; Régnard, P.; Corde, S.; Siegbahn, E.; LeDuc, G.; Brochard, T.; Blattmann, H.; Laissue, J.; Bravin, A.

    2005-07-01

    Microbeam radiation therapy (MRT) has the potential to treat infantile brain tumours when other kinds of radiotherapy would be excessively toxic to the developing normal brain. MRT uses extraordinarily high doses of x-rays but provides unusual resistance to radioneurotoxicity, presumably from the migration of endothelial cells from 'valleys' into 'peaks', i.e., into directly irradiated microslices of tissues. We present a novel irradiation geometry which results in a tolerable valley dose for the normal tissue and a decreased peak-to-valley dose ratio (PVDR) in the tumour area by applying an innovative cross-firing technique. We propose an MRT technique to orthogonally crossfire two arrays of parallel, nonintersecting, mutually interspersed microbeams that produces tumouricidal doses with small PVDRs where the arrays meet and tolerable radiation doses to normal tissues between the microbeams proximal and distal to the tumour in the paths of the arrays.

  16. Generating Composite Overlapping Grids on CAD Geometries

    SciTech Connect

    Henshaw, W.D.

    2002-02-07

    We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework.

  17. Quantization ambiguities in isotropic quantum geometry

    NASA Astrophysics Data System (ADS)

    Bojowald, Martin

    2002-10-01

    Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner. It is shown that these ambiguities do not affect the fate of the classical singularity, demonstrating that the absence of a singularity in loop quantum cosmology is a robust implication of the general quantization scheme. The calculations also allow conclusions about modified operators in the full theory. In particular, using holonomies in a non-fundamental representation of SU(2) to quantize connection components turns out to lead to significant corrections to classical behaviour at macroscopic volume for large values of the spin of the chosen representation.

  18. Parametric design and gridding through relational geometry

    NASA Technical Reports Server (NTRS)

    Letcher, John S., Jr.; Shook, D. Michael

    1995-01-01

    Relational Geometric Synthesis (RGS) is a new logical framework for building up precise definitions of complex geometric models from points, curves, surfaces and solids. RGS achieves unprecedented design flexibility by supporting a rich variety of useful curve and surface entities. During the design process, many qualitative and quantitative relationships between elementary objects may be captured and retained in a data structure equivalent to a directed graph, such that they can be utilized for automatically updating the complete model geometry following changes in the shape or location of an underlying object. Capture of relationships enables many new possibilities for parametric variations and optimization. Examples are given of panelization applications for submarines, sailing yachts, offshore structures, and propellers.

  19. Weyl semimetal and nonassociative Nambu geometry

    NASA Astrophysics Data System (ADS)

    Chu, Chong-Sun

    2016-03-01

    Topological materials are characterized by an electronic band structure with nontrivial topological properties. In this paper we introduce a basis of operators for the linear space of operators spanned by charge-neutral fermion bilinears. These band-projected density operators are constructed using directly the eigenfunctions of the electronic energy band structure and there is no need to assume a flat Berry curvature. As a result, our set of operators has a wider range of validity and is sensitive to physical phenomena which are not detectable in the flat-curvature limit. In particular, we show that the Berry monopole configuration of a Weyl semimetal give rises to a nonvanishing Jacobiator for these band-projected density operators, implying the emergence of nonassociativity at the location of the Weyl nodes. The resulting nonassociativity observes the fundamental identity, the defining property of the Nambu bracket, and so one may call this a nonassociative Nambu geometry. We also derive the corresponding uncertainty principle.

  20. Interferometric tests of Planckian quantum geometry models

    DOE PAGESBeta

    Kwon, Ohkyung; Hogan, Craig J.

    2016-04-19

    The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for nonstandard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographicmore » bounds on directional information. Lastly, predictions in this case are shown to be close to current and projected experimental bounds.« less

  1. Stochastic reasoning, free energy, and information geometry.

    PubMed

    Ikeda, Shiro; Tanaka, Toshiyuki; Amari, Shun-ichi

    2004-09-01

    Belief propagation (BP) is a universal method of stochastic reasoning. It gives exact inference for stochastic models with tree interactions and works surprisingly well even if the models have loopy interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. This article gives a unified framework for understanding BP and related methods and summarizes the results obtained in many fields. In particular, BP and its variants, including tree reparameterization and concave-convex procedure, are reformulated with information-geometrical terms, and their relations to the free energy function are elucidated from an information-geometrical viewpoint. We then propose a family of new algorithms. The stabilities of the algorithms are analyzed, and methods to accelerate them are investigated. PMID:15265322

  2. Realism, positivism, instrumentalism, and quantum geometry

    NASA Astrophysics Data System (ADS)

    Prugovečki, Eduard

    1992-02-01

    The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.

  3. Mannose-binding geometry of pradimicin A.

    PubMed

    Nakagawa, Yu; Doi, Takashi; Taketani, Takara; Takegoshi, K; Igarashi, Yasuhiro; Ito, Yukishige

    2013-08-01

    Pradimicins (PRMs) and benanomicins are the only family of non-peptidic natural products with lectin-like properties, that is, they recognize D-mannopyranoside (Man) in the presence of Ca(2+) ions. Coupled with their unique Man binding ability, they exhibit antifungal and anti-HIV activities through binding to Man-containing glycans of pathogens. Notwithstanding the great potential of PRMs as the lectin mimics and therapeutic leads, their molecular basis of Man recognition has yet to be established. Their aggregate-forming propensity has impeded conventional interaction analysis in solution, and the analytical difficulty is exacerbated by the existence of two Man binding sites in PRMs. In this work, we investigated the geometry of the primary Man binding of PRM-A, an original member of PRMs, by the recently developed analytical strategy using the solid aggregate composed of the 1:1 complex of PRM-A and Man. Evaluation of intermolecular distances by solid-state NMR spectroscopy revealed that the C2-C4 region of Man is in close contact with the primary binding site of PRM-A, while the C1 and C6 positions of Man are relatively distant. The binding geometry was further validated by co-precipitation experiments using deoxy-Man derivatives, leading to the proposal that PRM-A binds not only to terminal Man residues at the non-reducing end of glycans, but also to internal 6-substituted Man residues. The present study provides new insights into the molecular basis of Man recognition and glycan specificity of PRM-A. PMID:23832850

  4. Notes on "Quantum Gravity" and Noncommutative Geometry

    NASA Astrophysics Data System (ADS)

    Gracia-Bondía, J. M.

    I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Sect. 1.3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 1.4 briefly deals with the unimodular variants. Section 1.5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing, which justifies the place granted to the reconstruction theorem. Together with Sect. 1.3, this part constitutes the main body of the notes. Only very summarily at the end of this section do we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

  5. Interferometric probes of Planckian quantum geometry

    NASA Astrophysics Data System (ADS)

    Kwon, Ohkyung

    The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for non-standard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from Planck scale holographic bounds on directional information. Specific models of holographic spatial position states are adopted to predict mathematical characteristics of a possible quantum geometric departure from perfect coherence of a classical spacetime. Predictions in this case are shown to be close to current experimental bounds from GEO-600 and projected future sensitivity for the Fermilab Holometer. A model-independent statistical framework is also presented. This serves as a generalized method of data interpretation in systems such as the Fermilab Holometer, where the mean time derivative of positional cross correlation between world lines, a measure of geometrical quantum decoherence, is measured with a precision smaller than the Planck time. A parameterized candidate set of possible time domain correlation functions caused by holographic decoherence is shown to be consistent with the known causal structure of the classical geometry measured by an apparatus, and the holographic scaling of information suggested by gravity. Corresponding predicted frequency-domain power spectra are derived, and simple projections of sensitivity for specific interferometric set-ups show that measurements will directly yield constraints on a universal time derivative of the correlation function, and

  6. Geometry Shapes Evolution of Early Multicellularity

    PubMed Central

    Libby, Eric; Ratcliff, William; Travisano, Michael; Kerr, Ben

    2014-01-01

    Organisms have increased in complexity through a series of major evolutionary transitions, in which formerly autonomous entities become parts of a novel higher-level entity. One intriguing feature of the higher-level entity after some major transitions is a division of reproductive labor among its lower-level units in which reproduction is the sole responsibility of a subset of units. Although it can have clear benefits once established, it is unknown how such reproductive division of labor originates. We consider a recent evolution experiment on the yeast Saccharomyces cerevisiae as a unique platform to address the issue of reproductive differentiation during an evolutionary transition in individuality. In the experiment, independent yeast lineages evolved a multicellular “snowflake-like” cluster formed in response to gravity selection. Shortly after the evolution of clusters, the yeast evolved higher rates of cell death. While cell death enables clusters to split apart and form new groups, it also reduces their performance in the face of gravity selection. To understand the selective value of increased cell death, we create a mathematical model of the cellular arrangement within snowflake yeast clusters. The model reveals that the mechanism of cell death and the geometry of the snowflake interact in complex, evolutionarily important ways. We find that the organization of snowflake yeast imposes powerful limitations on the available space for new cell growth. By dying more frequently, cells in clusters avoid encountering space limitations, and, paradoxically, reach higher numbers. In addition, selection for particular group sizes can explain the increased rate of apoptosis both in terms of total cell number and total numbers of collectives. Thus, by considering the geometry of a primitive multicellular organism we can gain insight into the initial emergence of reproductive division of labor during an evolutionary transition in individuality. PMID:25233196

  7. Influence of geometry on liquid oxygen magnetohydrodynamics

    SciTech Connect

    Boulware, Jeffrey C.; Ban, Heng; Jensen, Scott; Wassom, Steve

    2010-11-15

    Magnetic fluid actuators have performed well in industrial applications, but have a limited temperature range due to the freezing point of the carrier fluid. Liquid oxygen (LOX) presents a pure, paramagnetic fluid suitable for use in a cryogenic magnetic fluid system; therefore, it is a potential solution to increasing the thermal range of magnetic fluid technology without the need for magnetic particles. The current study presents experimental work regarding the influence of geometry on the dynamics of a LOX slug in a 1.9 mm quartz tube when pulsed by a solenoid in a closed volume. A numerical analysis calculated the optimal solenoid geometry and balanced the magnetic, damping, and pressure forces to determine optimal slug lengths. Three configurations comprised the experiment: (1) a 24-gauge wire solenoid with an optimized 2.7 cm length slug, (2) a 30-gauge wire solenoid with an optimized 1.3 cm length slug, and (3) a 30-gauge wire solenoid with a nonoptimized 2.5 cm length slug. Typically, the hydrodynamic breakdown limit is calculated and used to determine the system range; however the experiment showed that the hydrodynamic breakdown limit was never reached by the slug. This implied that, instead, the system range should factor in a probabilistic risk of failure calculated as a function of the induced pressure change from its oscillations. The experimental data were also used to establish a nondimensional relationship between the maximum displacement and initial magnetic pressure on the slug. The average initial velocity of the slug was found to be proportional to the initial magnetic pressure, Mason number, and slug length. The results of this study can be used in the design and optimization of a LOX fluid system for space or low-temperature applications. (author)

  8. UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS

    SciTech Connect

    Broderick, Avery E.; Blandford, Roger D.

    2010-08-01

    Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m{sup -2}){sup 1/4}(B/1 G){sup 1/2} MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, {nu}{sub SA}, depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of {nu}{sub SA} range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, {nu}{sub SA} ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.

  9. Landscape as a Model: The Importance of Geometry

    PubMed Central

    Holland, E. Penelope; Aegerter, James N; Dytham, Calvin; Smith, Graham C

    2007-01-01

    In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models

  10. Fabric geometry distortion during composites processing

    NASA Technical Reports Server (NTRS)

    Chen, Julie

    1994-01-01

    Waviness and tow misalignment are often cited as possible causes of data scatter and lower compression stiffness and strength in textile composites. Strength differences of as much as 40 percent have been seen in composites that appear to have the same basic material and structural properties -- i.e., yarn orientation, yarn size, interlacing geometry. Fabric geometry distortion has been suggested as a possible reason for this discrepancy, but little quantitative data or substantial evidence exists. The focus of this research is to contribute to the present understanding of the causes and effects of geometric distortion in textile composites. The initial part of the study was an attempt to gather qualitative information on a variety of textile structures. Existing and new samples confirmed that structures with a significant direction presence would be more susceptible to distortion due to the compaction process. Thus, uniweaves (fiber vol frac: 54-72 percent) biaxial braids (vf: 34-58 percent) demonstrated very little fabric geometry distortion. In stitched panels, only slight buckling of z-direction stitches was observed, primarily near the surface. In contrast, for structures with high compaction ratios -- e.g., large cylindrical yarns (2.5:1) orpowder towpreg (4:1) -- there were visible distortions where previously smooth and periodic undulations were transformed to abrupt changes in direction. A controlled study of the effect of forming pressure on distortion was conducted on type 162 glass plain weave fabrics. Panels (6 x 6 in) were produced via a resin infusion type setup, but with an EPON 815 epoxy resin. Pressures ranging from hand layup to 200 psi were used (vf: 34-54 percent). Photomicrographs indicated that at pressures up to 50 psi, large changes in thickness were due primarily to resin squeeze out. At higher pressures, when intimate contact was made between the layers, there was some tow flattening and in-plane shifting to optimize nesting. However

  11. Optimal Geometry and Stimulating Mechanism of Deep-brain Electrode—Role of Electrode Contact Geometry

    NASA Astrophysics Data System (ADS)

    Lian, Qin; Wang, Jue; Liu, Hongzhong; Li, DiChen

    2008-09-01

    Deep brain stimulation has been demonstrated as an effective treatment for various locomotion disorders; however, the stimulating mechanism by which these high frequency electrical pulses intertwined with the geometry of electrode act on neuronal activity is unclear. Finite element analytic model of electrode in deep brain stimulation was established in this paper to investigate the impact of changes of electrode contact geometry on the cerebral electric field. The computational calculation showed that electrode contact configuration not only determined the stimulation position of electrode in the deep brain, but also played an important role on stimulated tissue area and stimulated field strength, which can provide more practical design rule for the electrode in deep brain stimulation.

  12. Influence of Nanostructure Geometry on Electronic Properties

    NASA Astrophysics Data System (ADS)

    Tavkhelidze, A.

    2014-06-01

    Recently, new quantum features have been studied in the area of nanostructured layers. It emerges that properties of nanostructures depend not only on their size but also on their geometry. Particularly, a nanograting (NG) on the surface of the thin layer imposes additional boundary conditions on electron wave function and forbids some quantum states. Density of quantum states reduces. Unlike conventional quantum well, state density per volume, is reduced in the case of NG layer. This leads to changes in electronic properties. Electrons, rejected from forbidden quantum states, have to occupy states with higher energy. In the case of semiconductor layers, electrons rejected from the valence band have to occupy empty quantum states in the conduction band. Such increase in conduction band electron concentration can be termed as geometry-induced doping or G-doping. G-doping is equivalent to donor doping from the point of view of the increase in electron concentration. However, there are no ionized impurities. This preserves charge carrier scattering to the intrinsic semiconductor level and increases carrier mobility with respect to the donor-doped layer. As rejected electrons occupy quantum states with the higher energy, the chemical potential of NG layer increases and becomes NG size dependent. We regard a system composed of NG layer and an additional layer on the top of the NG forming periodic series of p-n junctions. In such system, charge depletion region develops inside the top of NG and its effective height reduces, becoming a rather strong function of temperature T. Consequently, T-dependence of chemical potential magnifies and Seebeck coefficient S increases. Calculations show one order of magnitude increase in the thermoelectric figure of merit ZT relative to bulk material. In the case of metal layers, electrons rejected from forbidden quantum states below Fermi energy, occupy quantum states above Fermi energy. Fermi energy moves up on energy scale and work

  13. The Influence of Wildfire on Hillslope Geometry

    NASA Astrophysics Data System (ADS)

    Rengers, F. K.; Inbar, A.; Sheridan, G. J.; Nyman, P.

    2014-12-01

    In southeastern Australia wildfire occurs regularly, resulting in increased hillslope erosion. However, post-wildfire erosion processes differ depending on hillslope aspect. Equatorial (north)-facing slopes are drier than polar (south)-facing slopes and experience overland flow erosion after wildfire. By contrast, overland flow is not an active process on polar-facing slopes, even after high-intensity wildfires. These differences in post-wildfire erosion processes are accompanied by observations that slope angle and curvature also differ by hillslope aspect. An airborne LiDAR dataset flown over our study area in the Kinglake National Park, Victoria shows that the mean slope angle of polar-facing slopes is nearly 5 degrees steeper than equatorial-facing slopes. We have sought to test the hypothesis that aspect differences in post-wildfire erosion processes are sufficient to create differences in hillslope geometry. In order to test this hypothesis, we use a simple 1D model that simulates hillslope evolution over thousands of years. We limit our model to low-drainage area hillslopes where debris-flows are unlikely to occur. Erosion is modeled as nonlinear diffusion regardless of aspect during non-wildfire model years. Wildfire is modeled by changing the erosional processes on each slope aspect to reflect the effects of post-wildfire erosion according to a wildfire recurrence interval. For two years following a model wildfire we allow overland flow erosion to erode equatorial-facing slopes, whereas polar-facing slopes erode according to nonlinear diffusion for only one year following a wildfire. The erosion parameters on the polar-facing slopes are changed during this period to reflect higher post-wildfire erosion. In addition to erosional processes, we use an exponential soil production law to simulate new soil formation every model year. Our preliminary results suggest that changes in erosional magnitude associated with the different wildfire erosional processes are

  14. Acquisition of building geometry in the simulation of energy performance

    SciTech Connect

    Bazjanac, Vladimir

    2001-06-28

    Building geometry is essential to any simulation of building performance. This paper examines the importing of building geometry into simulation of energy performance from the users' point of view. It lists performance requirements for graphic user interfaces that input building geometry, and discusses the basic options in moving from two- to three-dimensional definition of geometry and the ways to import that geometry into energy simulation. The obvious answer lies in software interoperability. With the BLIS group of interoperable software one can interactively import building geometry from CAD into EnergyPlus and dramatically reduce the effort otherwise needed for manual input.The resulting savings may greatly increase the value obtained from simulation, the number of projects in which energy performance simulation is used, and expedite decision making in the design process.

  15. Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

    NASA Astrophysics Data System (ADS)

    De Gandt, François

    2006-06-01

    In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that "axiomatics", following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?

  16. The effect of geometry on integrity monitoring performance

    NASA Astrophysics Data System (ADS)

    Brown, Alison; Sturza, Mark

    A geometry parameter which can be utilized to define when receiver autonomous integrity monitoring is effective for each phase of flight is derived. The integrity geometry parameter permits the optimum geometry to be determined for maximizing the probability of failure detection and isolation in the presence of multiple instrument faults. These parameters can also be applied in evaluating the performance of redundant navigation systems in the presence of multiple or single instrument faults.

  17. Circular electrode geometry metal-semiconductor-metal photodetectors

    NASA Technical Reports Server (NTRS)

    Mcaddo, James A. (Inventor); Towe, Elias (Inventor); Bishop, William L. (Inventor); Wang, Liang-Guo (Inventor)

    1994-01-01

    The invention comprises a high speed, metal-semiconductor-metal photodetector which comprises a pair of generally circular, electrically conductive electrodes formed on an optically active semiconductor layer. Various embodiments of the invention include a spiral, intercoiled electrode geometry and an electrode geometry comprised of substantially circular, concentric electrodes which are interposed. These electrode geometries result in photodetectors with lower capacitances, dark currents and lower inductance which reduces the ringing seen in the optical pulse response.

  18. Circular electrode geometry metal-semiconductor-metal photodetectors

    NASA Technical Reports Server (NTRS)

    Mcadoo, James A. (Inventor); Towe, Elias (Inventor); Bishop, William L. (Inventor); Wang, Liang-Guo (Inventor)

    1995-01-01

    The invention comprises a high speed, metal-semiconductor-metal photodetector which comprises a pair of generally circular, electrically conductive electrodes formed on an optically active semiconductor layer. Various embodiments of the invention include a spiral, intercoiled electrode geometry and an electrode geometry comprised of substantially circular, concentric electrodes which are interposed. These electrode geometries result in photodetectors with lower capacitances, dark currents and lower inductance which reduces the ringing seen in the optical pulse response.

  19. Ideal spiral bevel gears: A new approach to surface geometry

    NASA Technical Reports Server (NTRS)

    Huston, R. L.; Coy, J. J.

    1980-01-01

    The fundamental geometrical characteristics of spiral bevel gear tooth surfaces are discussed. The parametric representation of an ideal spiral bevel tooth is developed based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics.

  20. Propagation of light in Schwarzschild geometry

    NASA Astrophysics Data System (ADS)

    Khorasani, Sina

    2010-02-01

    In this paper, the equivalent medium of Schwarzschild metric is discussed. The corresponding ray-tracing equations are integrated for the equivalent medium of the Schwarzschild geometry, which describes the curved space around a spherically symmetric, irrotational, and uncharged blackhole. We make comparison to the well-known expression by Einstein. While Einstein's estimate is reasonably good for large closest distances of approach to the star, it disregards the optical anisotropy of space. Instead, Virbhadra's estimate which takes the effects of anisotropy of Schwarzschild metric is shown to be more consistent with numerical simulations. Hence, a true physical anisotropy in the velocity of light under gravitational field does exist. We argue that the existence of such an optical anisotropy could be revealed exactly in the same way that the optical interferometry is expected to detect gravitational waves. Therefore, if no optical anisotropy under gravitational fields could be observed, then the possibility of interferometric detection of gravitational waves is automatically ruled out, and vice versa.

  1. Differential geometry of groups in string theory

    SciTech Connect

    Schmidke, W.B. Jr.

    1990-09-01

    Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1{vert bar}1). The quantum group GL{sub q}(1{vert bar}1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL{sub q}(1{vert bar}1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S{sup 1})/S{sup 1}. We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs.

  2. Planar geometry inertial electrostatic confinement fusion device

    NASA Astrophysics Data System (ADS)

    Knapp, Daniel R.

    2015-03-01

    In the classic gridded inertial electrostatic confinement (IEC) fusion reactor, ion bombardment of the grid leads to heating, thermionic electron emission, significant power loss, and ultimately melting of the grid. Gridless IEC devices have sought to overcome these limitations. Klein reported a gridless device in which ions are circulated as a linear beam in an electrostatic analogue of an optical resonator. To overcome limits of stored ions due to space charge effects at the turning regions, the device employed multiple overlapping traps. The work reported here seeks to further increase the turning region space in a gridless trap by employing a planar geometry. Ion trapping in the planar device was examined by simulating trajectories of 2H+ ions with SIMION 8.1 software. Simulations were carried out using multiple potentials as in Klein's device and for a single potential trap as a planar analogue of the anharmonic ion trap. Scattering by background gas was simulated using a hard sphere collision model, and the results suggested the device will require operation at low pressure with a separate ion source.

  3. Traffic Light Detection Using Conic Section Geometry

    NASA Astrophysics Data System (ADS)

    Hosseinyalmdary, S.; Yilmaz, A.

    2016-06-01

    Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.

  4. Optimized Geometry for Superconducting Sensing Coils

    NASA Technical Reports Server (NTRS)

    Eom, Byeong Ho; Pananen, Konstantin; Hahn, Inseob

    2008-01-01

    An optimized geometry has been proposed for superconducting sensing coils that are used in conjunction with superconducting quantum interference devices (SQUIDs) in magnetic resonance imaging (MRI), magnetoencephalography (MEG), and related applications in which magnetic fields of small dipoles are detected. In designing a coil of this type, as in designing other sensing coils, one seeks to maximize the sensitivity of the detector of which the coil is a part, subject to geometric constraints arising from the proximity of other required equipment. In MRI or MEG, the main benefit of maximizing the sensitivity would be to enable minimization of measurement time. In general, to maximize the sensitivity of a detector based on a sensing coil coupled with a SQUID sensor, it is necessary to maximize the magnetic flux enclosed by the sensing coil while minimizing the self-inductance of this coil. Simply making the coil larger may increase its self-inductance and does not necessarily increase sensitivity because it also effectively increases the distance from the sample that contains the source of the signal that one seeks to detect. Additional constraints on the size and shape of the coil and on the distance from the sample arise from the fact that the sample is at room temperature but the coil and the SQUID sensor must be enclosed within a cryogenic shield to maintain superconductivity.

  5. Uncertainty relations as Hilbert space geometry

    NASA Technical Reports Server (NTRS)

    Braunstein, Samuel L.

    1994-01-01

    Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

  6. Calculus and analytic geometry. Second edition

    SciTech Connect

    Mizrahi, A.; Sullivan, M.

    1986-01-01

    This book presents the details of calculus and analytic geometry. The topics covered are: Introduction. Real Numbers. Graphing. The Straight Line. Functions and Their Graphs. Operations on Functions; Types of Functions. Composite Functions. Inverse Functions. Limits from an Intuitive Point of View. Algebraic Techniques for Finding Limits. One-Sided Limits. Continuous Functions. Limit Theorems (If Time Permits). Historical Perspectives. The Derivative. Average Rate of Change. Instantaneous Rate of Change; the Derivative. Two Interpretations of the Derivative Formulas for Finding Derivatives. Formulas for Finding Derivatives (Continued). Higher-Order Derivatives. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivative of an Inverse Function; Rational Exponents. Newton's Method of Solving Equations. Functions that are not Differentiable at c., Applications of the Derivative. Related Rates. Differentials. Maxima and Minima. Rolle's Theorem; Mean Value Theorem. Increasing and Decreasing Functions; First Derivative Test. Concavity; Second Derivative Test. Limits at Infinity; Infinite Limits; Asymptotes. Applied Extrema Problems. Antiderivatives. Application to Economics (If Time Permits), The Definite Integral. Area. Evaluation of Area. The Definite Integral. The Fundamental Theorem of Calculus. Properties of the Definite Integral. The Indefinite Integral; Method of Substitution. Historical Perspectives. Applications of the Integral. Area. Volume of a Solid of Revolution: Disk Method. Volume of a Solid of Revolution: Shell Method. Volume by Slicing. Arc Length. Work. Liquid Pressure and Force. Average Value of a Function.

  7. Statistics and geometry of cosmic voids

    SciTech Connect

    Gaite, José

    2009-11-01

    We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distribution. Scaling voids with Pareto distribution appear in fractal distributions with box-counting dimension smaller than three (its maximum value), whereas the lognormal void distribution corresponds to multifractals with box-counting dimension equal to three. Moreover, voids of the former type persist in the continuum limit, namely, as the number density of observable objects grows, giving rise to lacunar fractals, whereas voids of the latter type disappear in the continuum limit, giving rise to non-lacunar (multi)fractals. We propose both lacunar and non-lacunar multifractal models of the cosmic web structure of the Universe. A non-lacunar multifractal model is supported by current galaxy surveys as well as cosmological N-body simulations. This model suggests, in particular, that small dark matter halos and, arguably, faint galaxies are present in cosmic voids.

  8. Accretion shock geometries in the magnetic variables

    NASA Technical Reports Server (NTRS)

    Stockman, H. S.

    1988-01-01

    The first self consistent shock models for the AM Herculis-type systems successfully identified the dominant physical processes and their signatures. These homogenous shock models predict unpolarized, Rayleigh-Jeans optical spectra with sharp cutoffs and rising polarizations as the shocks become optically thin in the ultraviolet. However, the observed energy distributions are generally flat with intermediate polarizations over a broad optical band. These and other observational evidence support a non-homogenous accretion profile which may extend over a considerable fraction of the stellar surface. Both the fundamental assumptions underlying the canonical 1-D shock model and the extension of this model to inhomogenous accretion shocks were identified, for both radial and linear structures. The observational evidence was also examined for tall shocks and little evidence was found for relative shock heights in excess of h/R(1) greater than or equal to 0.1. For several systems, upper limits to the shock height can be obtained from either x ray or optical data. These lie in the region h/R(1) is approximately 0.01 and are in general agreement with the current physical picture for these systems. The quasi-periodic optical variations observed in several magnetic variables may eventually prove to be a major aid in further understanding their accretion shock geometries.

  9. Linquistic geometry: new technology for decision support

    NASA Astrophysics Data System (ADS)

    Stilman, Boris; Yakhnis, Vladimir

    2003-09-01

    Linguistic Geometry (LG) is a revolutionary gaming approach which is ideally suited for military decision aids for Air, Ground, Naval, and Space-based operations, as well guiding robotic vehicles and traditional entertainment games. When thinking about modern or future military operations, the game metaphor comes to mind right away. Indeed, the air space together with the ground and seas may be viewed as a gigantic three-dimensional game board. Refining this picture, the LG approach is capable of providing an LG hypergame, that is, a system of multiple concurrent interconnected multi-player abstract board games (ABG) of various resolutions and time frames reflecting various kinds of hardware and effects involved in the battlespace and the solution space. By providing a hypergame representation of the battlespace, LG already provides a significant advance in situational awareness. However, the greatest advantage of the LG approach is an ability to provide commanders of campaigns and missions with decision options resulting in attainment of the commander's intent. At each game turn, an LG decision support tool assigns the best actions to each of the multitude of battlespace actors (UAVs, bombers, cruise missiles, etc.). This is done through utilization of algorithms finding winning strategies and tactics, which are the core of the LG approach.

  10. Discrete differential geometry: The nonplanar quadrilateral mesh

    NASA Astrophysics Data System (ADS)

    Twining, Carole J.; Marsland, Stephen

    2012-06-01

    We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

  11. Discrete differential geometry: the nonplanar quadrilateral mesh.

    PubMed

    Twining, Carole J; Marsland, Stephen

    2012-06-01

    We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids. PMID:23005244

  12. Strain Functionals for Characterizing Atomistic Geometries

    NASA Astrophysics Data System (ADS)

    Kober, Edward; Rudin, Sven

    The development of a set of strain tensor functionals that are capable of characterizing arbitrarily ordered atomistic structures is described. This approach defines a Gaussian-weighted neighborhood around each atom and characterizes that local geometry in terms of n-th order strain tensors, which are equivalent to the moments of the neighborhood. Fourth order expansions can distinguish the cubic structures (and deformations thereof), but sixth order expansions are required to fully characterize hexagonal structures. Other methods used to characterize atomic structures, such as the Steinhardt parameters or the centrosymmetry metric, can be derived from this more general approach. These functions are continuous and smooth and much less sensitive to thermal fluctuations than other descriptors based on discrete neighborhoods. They allow material phases, deformations, and a large number of defect structures to be readily identified and classified. Applications to the analysis of shock-loaded samples of Cu, Ta and Ti will be presented. This strain functional basis can also then be used for developing interatomic potential functions, and an initial application to Cu will be presented.

  13. Domain wall geometry controls conduction in ferroelectrics.

    PubMed

    Vasudevan, R K; Morozovska, A N; Eliseev, E A; Britson, J; Yang, J-C; Chu, Y-H; Maksymovych, P; Chen, L Q; Nagarajan, V; Kalinin, S V

    2012-11-14

    A new paradigm of domain wall nanoelectronics has emerged recently, in which the domain wall in a ferroic is itself an active device element. The ability to spatially modulate the ferroic order parameter within a single domain wall allows the physical properties to be tailored at will and hence opens vastly unexplored device possibilities. Here, we demonstrate via ambient and ultrahigh-vacuum (UHV) scanning probe microscopy (SPM) measurements in bismuth ferrite that the conductivity of the domain walls can be modulated by up to 500% in the spatial dimension as a function of domain wall curvature. Landau-Ginzburg-Devonshire calculations reveal the conduction is a result of carriers or vacancies migrating to neutralize the charge at the formed interface. Phase-field modeling indicates that anisotropic potential distributions can occur even for initially uncharged walls, from polarization dynamics mediated by elastic effects. These results are the first proof of concept for modulation of charge as a function of domain wall geometry by a proximal probe, thereby expanding potential applications for oxide ferroics in future nanoscale electronics. PMID:22994244

  14. Role of target geometry in phagocytosis

    PubMed Central

    Champion, Julie A.; Mitragotri, Samir

    2006-01-01

    Phagocytosis is a principal component of the body’s innate immunity in which macrophages internalize targets in an actin-dependent manner. Targets vary widely in shape and size and include particles such as pathogens and senescent cells. Despite considerable progress in understanding this complicated process, the role of target geometry in phagocytosis has remained elusive. Previous studies on phagocytosis have been performed using spherical targets, thereby overlooking the role of particle shape. Using polystyrene particles of various sizes and shapes, we studied phagocytosis by alveolar macrophages. We report a surprising finding that particle shape, not size, plays a dominant role in phagocytosis. All shapes were capable of initiating phagocytosis in at least one orientation. However, the local particle shape, measured by tangent angles, at the point of initial contact dictates whether macrophages initiate phagocytosis or simply spread on particles. The local shape determines the complexity of the actin structure that must be created to initiate phagocytosis and allow the membrane to move over the particle. Failure to create the required actin structure results in simple spreading and not internalization. Particle size primarily impacts the completion of phagocytosis in cases where particle volume exceeds the cell volume. PMID:16549762

  15. Effective geometry of a white dwarf

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.

    2011-03-15

    The ''effective geometry'' formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties, manifested instead by polytropic stars, and requires a parametric study of the solutions both at the numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Pade type, which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing general perturbations following Chebsch's formalism. Even in this quantum case, the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on nonquantum self-gravitating polytropic stars. The equations of the theory are finally numerically integrated in the simpler case of irrotational spherical pulsating perturbations, including the effect of backreaction, in order to have a dynamical picture of the process occurring in the acoustic metric.

  16. Geometry of Calabi-Yau Moduli

    NASA Astrophysics Data System (ADS)

    Yin, Changyong

    In this thesis, we study the geometry of the moduli space and the Teichmuller space of Calabi-Yau manifolds, which mainly involves the following two aspects: the (locally, globally) Hermitian symmetric property of the Teichmuller space and the first Chern form of the moduli space with the Weil-Petersson and Hodge metrics. In the first part, we define the notation of quantum correction for the Teichmuller space T of Calabi-Yau manifolds. Under the assumption of vanishing of weak quantum correction, we prove that the Teichmuller space, with the Weil-Petersson metric, is a locally symmetric space. For Calabi-Yau threefolds, we show that the vanishing of strong quantum correction is equivalent to that the image of the Teichmuller space under the period map is an open submanifold of a globally Hermitian symmetric space W of the same dimension as T. Finally, for Hyperkahler manifolds of dimension 2n ≥ 4, we find globally defined families of (2, 0) and (2n, 0)-classes over the Teichmuller space of polarized Hyperkahler manifolds. In the second part, we prove that the first Chern form of the moduli space of polarized Calabi-Yau manifolds, with the Hodge metric or the Weil-Petersson metric, represents the first Chern class of the canonical extensions of the tangent bundle to the compactification of the moduli space with normal crossing divisors.

  17. Massive neutrinos in almost-commutative geometry

    NASA Astrophysics Data System (ADS)

    Stephan, Christoph A.

    2007-02-01

    In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), e-print hep-th/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), e-print hep-th-9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

  18. Massive neutrinos in almost-commutative geometry

    SciTech Connect

    Stephan, Christoph A.

    2007-02-15

    In the noncommutative formulation of the standard model of particle physics by Chamseddine and Connes [Commun. Math. Phys. 182, 155 (1996), e-print hep-th/9606001], one of the three generations of fermions has to possess a massless neutrino. [C. P. Martin et al., Phys. Rep. 29, 363 (1998), e-print hep-th-9605001]. This formulation is consistent with neutrino oscillation experiments and the known bounds of the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix). But future experiments which may be able to detect neutrino masses directly and high-precision measurements of the PMNS matrix might need massive neutrinos in all three generations. In this paper we present an almost-commutative geometry which allows for a standard model with massive neutrinos in all three generations. This model does not follow in a straightforward way from the version of Chamseddine and Connes since it requires an internal algebra with four summands of matrix algebras, instead of three summands for the model with one massless neutrino.

  19. Vesicle Geometries Enabled by Dynamically Trapped States.

    PubMed

    Su, Jiaye; Yao, Zhenwei; de la Cruz, Monica Olvera

    2016-02-23

    Understanding and controlling vesicle shapes is a fundamental challenge in biophysics and materials design. In this paper, we design dynamic protocols for enlarging the shape space of both fluid and crystalline vesicles beyond the equilibrium zone. By removing water from within the vesicle at different rates, we numerically produced a series of dynamically trapped stable vesicle shapes for both fluid and crystalline vesicles in a highly controllable fashion. In crystalline vesicles that are continuously dehydrated, simulations show the initial appearance of small flat areas over the surface of the vesicles that ultimately merge to form fewer flat faces. In this way, the vesicles transform from a fullerene-like shape into various faceted polyhedrons. We perform analytical elasticity analysis to show that these salient features are attributable to the crystalline nature of the vesicle. The potential to use dynamic protocols, such as those used in this study, to engineer vesicle shape transformations is helpful for exploiting the richness of vesicle geometries for desired applications. PMID:26795199

  20. Effects of flow geometry on blood viscoelasticity.

    PubMed

    Thurston, George B; Henderson, Nancy M

    2006-01-01

    The viscoelastic properties of blood are dominated by microstructures formed by red cells. The microstructures are of several types such as irregular aggregates, rouleaux, and layers of aligned cells. The dynamic deformability of the red cells, aggregation tendency, cell concentration, size of confining vessel and rate of flow are determining factors in the microstructure. Viscoelastic properties, viscosity and elasticity, relate to energy loss and storage in flowing blood while relaxation time and Weissenberg number play a role in assessing the importance of the elasticity relative to the viscosity. These effects are shown herein for flow in a large straight cylindrical tube, a small tube, and a porous medium. These cases approximate the geometries of the arterial system: large vessels, small vessels and vessels with many branches and bifurcations. In each case the viscosity, elasticity, relaxation time and Weissenberg number for normal human blood as well as blood with enhanced cell aggregation tendency and diminished cell deformability are given. In the smaller spaces of the microtubes and porous media, the diminished viscosity shows the possible influence of the Fåhraeus-Lindqvist effect and at high shear rates, the viscoelasticity of blood shows dilatancy. This is true for normal, aggregation enhanced and hardened cells. PMID:17148856

  1. 3D geometry applied to atmospheric layers

    NASA Astrophysics Data System (ADS)

    Nadjib Kouahla, Mohamed; Moreels, Guy; Faivre, Michael

    Epipolar geometry is an efficient method for generating 3D representations of objects. Here we present an original application of this method to the case of atmospheric layers. Two synchronized simultaneous images of the same scene are taken in two sites at a distance D. The 36*36 fields of view are oriented face to face along the same line of sight, but in opposite directions. The elevation angle of the optical axis above the horizon is 17. The observed objects are airglow emissions or cirrus clouds or aircraft trails. In the case of clouds, the shape of the objects is diffuse. To obtain a superposition of the common observed zone, it is necessary to calculate a normalized cross-correlation coefficient (NCC) to identify pairs of matching points in both images. The perspective effect in the rectangular images is inverted to produce a satellite-type view of the atmospheric layer as could be seen from an overlying satellite. We developed a triangulation algorithm to retrieve the 3D surface of the observed layer. The stereoscopic method was used to retrieve the wavy structure of the OH emissive layer at the altitude of 87 km. The distance between the observing sites was 600 km. Results obtained in Peru from the sites of Cerro Cosmos and Cerro Verde will be presented. We are currently extending the stereoscopic procedure to the study of troposphere cirruses, of natural origin or induced by aircraft engines. In this case, the distance between observation sites is D 60 km.

  2. Aerodynamic characteristics of scissor-wing geometries

    NASA Technical Reports Server (NTRS)

    Selberg, Bruce P.; Rokhsaz, Kamran; Housh, Clinton S.

    1991-01-01

    A scissor-wing configuration, consisting of two independently sweeping-wing surfaces, is compared with an equivalent fixed-wing geometry baseline over a wide Mach number range. The scissor-wing configuration is shown to have a higher total lift-to-drag ratio than the baseline in the subsonic region primarily due to the slightly higher aspect ratio of the unswept scissor wing. In the transonic region, the scissor wing is shown to have a higher lift-to-drag ratio than the baseline for values of lift coefficient greater than 0.35. It is also shown that, through the use of wing decalage, the lift of the two independent scissor wings can be equalized. In the supersonic regime, the zero lift wave drag of the scissor-wing at maximum sweep is shown to be 50 and 28 percent less than the zero lift wave drag of the baseline at Mach numbers 1.5 and 3.0, respectively. In addition, a pivot-wing configuration is introduced and compared with the scissor wing. The pivot-wing configuration is shown to have a slightly higher total lift-to-drag ratio than the scissor wing in the supersonic region due to the decreased zero lift wave drag of the pivot-wing configuration.

  3. Geometry creation for MCNP by Sabrina and XSM

    SciTech Connect

    Van Riper, K.A.

    1994-02-01

    The Monte Carlo N-Particle transport code MCNP is based on a surface description of 3-dimensional geometry. Cells are defined in terms of boolean operations on signed quadratic surfaces. MCNP geometry is entered as a card image file containing coefficients of the surface equations and a list of surfaces and operators describing cells. Several programs are available to assist in creation of the geometry specification, among them Sabrina and the new ``Smart Editor`` code XSM. We briefly describe geometry creation in Sabrina and then discuss XSM in detail. XSM is under development; our discussion is based on the state of XSM as of January 1, 1994.

  4. Remarks on Hamiltonian structures in G{sub 2}-geometry

    SciTech Connect

    Cho, Hyunjoo Salur, Sema; Todd, A. J.

    2013-12-15

    In this article, we treat G{sub 2}-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G{sub 2}-structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G{sub 2}-structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry.

  5. PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

    NASA Astrophysics Data System (ADS)

    Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

    2009-10-01

    Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex dynamics, solvable models of statistical physics, deformation quantization, and many others. Soliton theory now forms a beautiful part of mathematics with very strong physical motivations and numerous applications. Interactions between mathematics and physics associated with integrability issues are very fruitful and stimulating. For instance, spectral theories of linear quantum mechanics turned out to be crucial for studying nonlinear integrable systems. The modern theory of integrable nonlinear partial differential and difference equations, or the `theory of solitons', is deeply rooted in the achievements of outstanding geometers of the end of the 19th and the beginning of the 20th century, such as Luigi Bianchi (1856-1928) and Jean Gaston Darboux (1842-1917). Transformations of surfaces and explicit constructions developed by `old' geometers were often rediscovered or reinterpreted in a modern framework. The great progress of recent years in so-called discrete geometry is certainly due to strong integrable motivations. A very remarkable feature of the results of the classical integrable geometry is the quite natural (although nontrivial) possibility of their discretization. This special issue is dedicated to Jean Gaston Darboux and his pioneering role in the development of the geometric ideas of modern soliton theory. The most famous aspects of his work are probably Darboux transformations and triply orthogonal systems of surfaces, whose role in modern mathematical physics cannot be overestimated. Indeed, Darboux transformations play a central

  6. The Planetary Data System Information Model for Geometry Metadata

    NASA Astrophysics Data System (ADS)

    Guinness, E. A.; Gordon, M. K.

    2014-12-01

    The NASA Planetary Data System (PDS) has recently developed a new set of archiving standards based on a rigorously defined information model. An important part of the new PDS information model is the model for geometry metadata, which includes, for example, attributes of the lighting and viewing angles of observations, position and velocity vectors of a spacecraft relative to Sun and observing body at the time of observation and the location and orientation of an observation on the target. The PDS geometry model is based on requirements gathered from the planetary research community, data producers, and software engineers who build search tools. A key requirement for the model is that it fully supports the breadth of PDS archives that include a wide range of data types from missions and instruments observing many types of solar system bodies such as planets, ring systems, and smaller bodies (moons, comets, and asteroids). Thus, important design aspects of the geometry model are that it standardizes the definition of the geometry attributes and provides consistency of geometry metadata across planetary science disciplines. The model specification also includes parameters so that the context of values can be unambiguously interpreted. For example, the reference frame used for specifying geographic locations on a planetary body is explicitly included with the other geometry metadata parameters. The structure and content of the new PDS geometry model is designed to enable both science analysis and efficient development of search tools. The geometry model is implemented in XML, as is the main PDS information model, and uses XML schema for validation. The initial version of the geometry model is focused on geometry for remote sensing observations conducted by flyby and orbiting spacecraft. Future releases of the PDS geometry model will be expanded to include metadata for landed and rover spacecraft.

  7. Singularities and the geometry of spacetime

    NASA Astrophysics Data System (ADS)

    Hawking, Stephen

    2014-11-01

    The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

  8. The geochemical geometry of mantle plumes

    NASA Astrophysics Data System (ADS)

    Jackson, Matthew

    2015-04-01

    , and a clear relationship emerges from the dataset. This observation supports a hypothesis where several low-3He/4He components are embedded within (and mix with) a plume matrix that is composed of the high 3He/4He component. In this way, the four distinct Pb-isotopic groups do not mix efficiently with each other, thereby preserving the four distinct arrays in Pb-isotope space. However, the low 3He/4He components do mix with the high 3He/4He plume matrix, thereby generating the clear relationship between He and Pb isotopes. These mixing relationships provide a clear picture of the geochemical geometry of the Samoan plume. However, owing to the sparse datasets that link high-precision Pb-isotopic measurements with 3He/4He measurements on the same sample, it is not yet clear whether the geochemical geometry observed in the Samoan plume is feature that is common to mantle plumes globally.

  9. Geometry of thin liquid sheet flows

    NASA Technical Reports Server (NTRS)

    Chubb, Donald L.; Calfo, Frederick D.; Mcconley, Marc W.; Mcmaster, Matthew S.; Afjeh, Abdollah A.

    1994-01-01

    Incompresible, thin sheet flows have been of research interest for many years. Those studies were mainly concerned with the stability of the flow in a surrounding gas. Squire was the first to carry out a linear, invicid stability analysis of sheet flow in air and compare the results with experiment. Dombrowski and Fraser did an experimental study of the disintegration of sheet flows using several viscous liquids. They also detected the formulation of holes in their sheet flows. Hagerty and Shea carried out an inviscid stability analysis and calculated growth rates with experimental values. They compared their calculated growth rates with experimental values. Taylor studied extensively the stability of thin liquid sheets both theoretically and experimentally. He showed that thin sheets in a vacuum are stable. Brown experimentally investigated thin liquid sheet flows as a method of application of thin films. Clark and Dumbrowski carried out second-order stability analysis for invicid sheet flows. Lin introduced viscosity into the linear stability analysis of thin sheet flows in a vacuum. Mansour and Chigier conducted an experimental study of the breakup of a sheet flow surrounded by high-speed air. Lin et al. did a linear stability analysis that included viscosity and a surrounding gas. Rangel and Sirignano carried out both a linear and nonlinear invisid stability analysis that applies for any density ratio between the sheet liquid and the surrounding gas. Now there is renewed interest in sheet flows because of their possible application as low mass radiating surfaces. The objective of this study is to investigate the fluid dynamics of sheet flows that are of interest for a space radiator system. Analytical expressions that govern the sheet geometry are compared with experimental results. Since a space radiator will operate in a vacuum, the analysis does not include any drag force on the sheet flow.

  10. Interferometers as probes of Planckian quantum geometry

    NASA Astrophysics Data System (ADS)

    Hogan, Craig J.

    2012-03-01

    A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, tP. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wave functions in two dimensions displays a new kind of directionally coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wave functions on a 2D space-like surface with the entropy density of a black hole event horizon of the same area. In a region of size L, the effect resembles spatially and directionally coherent random transverse shear deformations on time scale ≈L/c with typical amplitude ≈ctPL. This quantum-geometrical “holographic noise” in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beam splitter for durations up to the light-crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly colocated Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.

  11. Numerical geometry of map and model assessment.

    PubMed

    Wriggers, Willy; He, Jing

    2015-11-01

    We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8Å) and medium (4-8 Å) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naïve vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent. PMID:26416532

  12. A computer program for analyzing channel geometry

    USGS Publications Warehouse

    Regan, R.S.; Schaffranek, R.W.

    1985-01-01

    The Channel Geometry Analysis Program (CGAP) provides the capability to process, analyze, and format cross-sectional data for input to flow/transport simulation models or other computational programs. CGAP allows for a variety of cross-sectional data input formats through use of variable format specification. The program accepts data from various computer media and provides for modification of machine-stored parameter values. CGAP has been devised to provide a rapid and efficient means of computing and analyzing the physical properties of an open-channel reach defined by a sequence of cross sections. CGAP 's 16 options provide a wide range of methods by which to analyze and depict a channel reach and its individual cross-sectional properties. The primary function of the program is to compute the area, width, wetted perimeter, and hydraulic radius of cross sections at successive increments of water surface elevation (stage) from data that consist of coordinate pairs of cross-channel distances and land surface or channel bottom elevations. Longitudinal rates-of-change of cross-sectional properties are also computed, as are the mean properties of a channel reach. Output products include tabular lists of cross-sectional area, channel width, wetted perimeter, hydraulic radius, average depth, and cross-sectional symmetry computed as functions of stage; plots of cross sections; plots of cross-sectional area and (or) channel width as functions of stage; tabular lists of cross-sectional area and channel width computed as functions of stage for subdivisions of a cross section; plots of cross sections in isometric projection; and plots of cross-sectional area at a fixed stage as a function of longitudinal distance along an open-channel reach. A Command Procedure Language program and Job Control Language procedure exist to facilitate program execution on the U.S. Geological Survey Prime and Amdahl computer systems respectively. (Lantz-PTT)

  13. Downstream Hydraulic Geometry of Mountain Rivers

    NASA Astrophysics Data System (ADS)

    Wohl, E.

    2003-12-01

    The concept of downstream hydraulic geometry (DHG) was developed for fully alluvial rivers that are presumed to be capable of continually adjusting their dimensions to changes in bankfull discharge. Mountain rivers, although mostly formed in alluvium, may behave differently because discharges along the channel lack the competence to move coarse clasts introduced from colluvial processes or glaciation, or because discontinuous bedrock exposures limit channel adjustment. Consequently, the DHG of mountain rivers could reflect bankfull flows; larger magnitude, less frequent flows; or non-fluvial processes such as debris flows. The research summarized here was designed to test whether traditional DHG concepts apply to mountain rivers, and to determine when correlations between velocity, flow depth, or width, and bankfull discharge, are strongly developed. Rivers with strongly developed DHG are defined here as those with r2 values > 0.5 for at least two of the correlations. I hypothesize that a quantifiable threshold separates mountain rivers with well-developed DHG from those with poorly-developed DHG. This threshold can be expressed using a ratio of hydraulic driving forces to substrate resisting forces. As the ratio increases, the ability of bankfull flows to adjust channel dimensions should also increase. The hypothesis was tested using 8 datasets from mountain rivers in Alaska, Montana, Colorado, Panama, Nepal, and New Zealand. A ratio of either total stream power/D84, or unit stream power/D84, separates rivers with and without well-developed DHG. This approach is a simplification which ignores the presence of bedrock; the duration and frequency of flows as these affect stream power; and non-fluvial processes. However, the results suggest that mountain rivers with greater hydraulic driving forces are more likely to behave like fully alluvial rivers in terms of having well-developed DHG relations.

  14. Measuring intranodal pressure and lymph viscosity to elucidate mechanisms of arthritic flare and therapeutic outcomes

    PubMed Central

    Bouta, Echoe M.; Wood, Ronald W.; Perry, Seth W.; Brown, Edward; Ritchlin, Christopher T.; Xing, Lianping; Schwarz, Edward M.

    2012-01-01

    Rheumatoid arthritis (RA) is a chronic autoimmune disease with episodic flares in affected joints, whose etiology is largely unknown. Recent studies in mice demonstrated alterations in lymphatics from affected joints precede flares. Thus, we aimed to develop novel methods for measuring lymph node pressure and lymph viscosity in limbs of mice. Pressure measurements were performed by inserting a glass micropipette connected to a pressure transducer into popliteal lymph nodes (PLN) or axillary lymph nodes (ALN) of mice and determined that the lymphatic pressures were 9 and 12 cm of water, respectively. We are also developing methods for measuring lymph viscosity in lymphatic vessels afferent to PLN, which can be measured by multi-photon fluorescence recovery after photobleaching (MP-FRAP) of FITC-BSA injected into the hind footpad. These results demonstrate the potential of lymph node pressure and lymph viscosity measurements, and warrant future studies to test these outcomes as biomarkers of arthritic flare. PMID:22172039

  15. Simplifying and speeding the management of intra-node cache coherence

    DOEpatents

    Blumrich, Matthias A.; Chen, Dong; Coteus, Paul W.; Gara, Alan G.; Giampapa, Mark E.; Heidelberger, Phillip; Hoenicke, Dirk; Ohmacht, Martin

    2012-04-17

    A method and apparatus for managing coherence between two processors of a two processor node of a multi-processor computer system. Generally the present invention relates to a software algorithm that simplifies and significantly speeds the management of cache coherence in a message passing parallel computer, and to hardware apparatus that assists this cache coherence algorithm. The software algorithm uses the opening and closing of put/get windows to coordinate the activated required to achieve cache coherence. The hardware apparatus may be an extension to the hardware address decode, that creates, in the physical memory address space of the node, an area of virtual memory that (a) does not actually exist, and (b) is therefore able to respond instantly to read and write requests from the processing elements.

  16. Using Dynamic Geometry to Explore Non-Traditional Theorems

    ERIC Educational Resources Information Center

    Wares, Arsalan

    2010-01-01

    The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

  17. Using 3D Geometric Models to Teach Spatial Geometry Concepts.

    ERIC Educational Resources Information Center

    Bertoline, Gary R.

    1991-01-01

    An explanation of 3-D Computer Aided Design (CAD) usage to teach spatial geometry concepts using nontraditional techniques is presented. The software packages CADKEY and AutoCAD are described as well as their usefulness in solving space geometry problems. (KR)

  18. Teachers Modify Geometry Problems: From Proof to Investigation

    ERIC Educational Resources Information Center

    Leikin, Roza; Grossman, Dorith

    2013-01-01

    We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

  19. Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

    ERIC Educational Resources Information Center

    Trocki, Aaron

    2014-01-01

    The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…

  20. LDEF geometry/mass model for radiation analyses

    NASA Technical Reports Server (NTRS)

    Colborn, B. L.; Armstrong, T. W.

    1992-01-01

    A three-dimensional geometry/mass model of LDEF is under development for ionizing radiation analyses. This model, together with ray tracing algorithms, is being programmed for use both as a stand alone code in determining three-dimensional shielding distributions at dosimetry locations and as a geometry module that can be interfaced with radiation transport codes.

  1. New Opportunities in Geometry Education at the Primary School

    ERIC Educational Resources Information Center

    Sinclair, Nathalie; Bruce, Catherine D.

    2015-01-01

    This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of…

  2. Geometry and Thermodynamics: Exploring the Internal Energy Landscape

    ERIC Educational Resources Information Center

    Hantsaridou, A. P.; Polatoglou, H. M.

    2006-01-01

    If we look into the past we will discover that the teachers of thermodynamics were always trying to interpret an important part of their science by using geometry. The relation between geometry and thermodynamics is of great interest and importance in teaching thermodynamics. This article examines the way undergraduate students of thermodynamics…

  3. Using Dynamic Geometry Software To Simulate Physical Motion.

    ERIC Educational Resources Information Center

    Gonzalez-Lopez, Maria Jose

    2001-01-01

    Analyzes to what extent the computational model of the geometry implemented in a dynamic geometry environment provides models for physical motion, focusing on the continuity issues related to motion. Addresses the issue of the computable representation of knowledge. (Author/MM)

  4. Theory of Alfven wave heating in general toroidal geometry

    SciTech Connect

    Tataronis, J.A.; Salat, A.

    1981-09-01

    A general treatment of Alfven wave heating based on the linearized equations of ideal magnetohydrodynamics (MHD) is given. The conclusion of this study is that the geometry of the plasma equilium could play an important role on the effectiveness of this heating mechanism, and for certain geometries the fundamental equations may not possess solutions which satisfy prescribed boundary conditions.

  5. Space and Geometry. Papers from a Research Workshop.

    ERIC Educational Resources Information Center

    Martin, J. Larry, Ed.; Bradbard, David A., Ed.

    Seven papers presented at a research conference on space and geometry are contained in this monograph. The first paper gives an historical sketch of the development of geometry and discusses several considerations for selecting geometric content for the elementary school. Two papers deal with Piaget's research into the child's development of space…

  6. Sensitivity analysis of imaging geometries for prostate diffuse optical tomography

    NASA Astrophysics Data System (ADS)

    Zhou, Xiaodong; Zhu, Timothy C.

    2008-02-01

    Endoscopic and interstitial diffuse optical tomography have been studied in clinical investigations for imaging prostate tissues, yet, there is no comprehensive comparison of how these two imaging geometries affect the quality of the reconstruction images. In this study, the effect of imaging geometry is investigated by comparing the cross-section of the Jacobian sensitivity matrix and reconstructed images for three-dimensional mathematical phantoms. Next, the effect of source-detector configurations and number of measurements in both geometries is evaluated using singular value analysis. The amount of information contained for each source-detector configuration and different number of measurements are compared. Further, the effect of different measurements strategies for 3D endoscopic and interstitial tomography is examined. The pros and cons of using the in-plane measurements and off-plane measurements are discussed. Results showed that the reconstruction in the interstitial geometry outperforms the endoscopic geometry when deeper anomalies are present. Eight sources 8 detectors and 6 sources 12 detectors are sufficient for 2D reconstruction with endoscopic and interstitial geometry respectively. For a 3D problem, the quantitative accuracy in the interstitial geometry is significantly improved using off-plane measurements but only slightly in the endoscopic geometry.

  7. MISR Camera Geometry Model (MISANCGM_V2)

    NASA Technical Reports Server (NTRS)

    Diner, David J. (Principal Investigator)

    The CGM dataset is used to describe pointing geometry of the nine MISR cameras. It consists of a set of parameters used in a mathematical expression that gives the pointing direction of an arbitrary pixel in the spacecraft attitude frame of reference. These parameters represent the geometry of the camera system and account for distortions from an ideal optical system..

  8. From geometry to algebra: the Euclidean way with technology

    NASA Astrophysics Data System (ADS)

    Ferrarello, Daniela; Flavia Mammana, Maria; Pennisi, Mario

    2016-05-01

    In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.

  9. The Role of Structure in Learning Non-Euclidean Geometry

    ERIC Educational Resources Information Center

    Asmuth, Jennifer A.

    2009-01-01

    How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically…

  10. The relationship between sensor geometry, vegetation-canopy geometry and image variance

    NASA Astrophysics Data System (ADS)

    Barnsley, M. J.; Kay, S. A. W.

    1990-06-01

    The geometry of the sensor and the vegetation canopy have an effect upon the variance of the detected spectral response of a single cover type in an image. The procedure for calculating the size of the ground resolution element (GRE) for a Daedalus ATM scanner is outlined, and examples of changes in variance for four land-cover types are presented. Image variance was found to be inversely related to sensor view angle, owing to the increased size of the GRE, the increased overlap of adjacent elements, and the changing proportions of canopy components viewed by the sensor.

  11. Lensless x-ray imaging in reflection geometry

    SciTech Connect

    Roy, S.; Parks, D.H.; Seu, K.A.; Turner, J.J.; Chao, W.; Anderson, E.H.; Cabrini, S.; Kevan, S.D.; Su, R.

    2011-02-03

    Lensless X-ray imaging techniques such as coherent diffraction imaging and ptychography, and Fourier transform holography can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have focused on transmission geometry, restricting the samples and reciprocal spaces that can be investigated. We report a lensless X-ray technique developed for imaging in Bragg and small-angle scattering geometries, which may also find application in transmission geometries. We demonstrate this by imaging a nanofabricated pseudorandom binary structure in small-angle reflection geometry. The technique can be used with extended objects, places no restriction on sample size, and requires no additional sample masking. The realization of X-ray lensless imaging in reflection geometry opens up the possibility of single-shot imaging of surfaces in thin films, buried interfaces in magnetic multilayers, organic photovoltaic and field-effect transistor devices, or Bragg planes in a single crystal.

  12. Geometry Description Markup Language for Physics Simulation And Analysis Applications.

    SciTech Connect

    Chytracek, R.; McCormick, J.; Pokorski, W.; Santin, G.; /European Space Agency

    2007-01-23

    The Geometry Description Markup Language (GDML) is a specialized XML-based language designed as an application-independent persistent format for describing the geometries of detectors associated with physics measurements. It serves to implement ''geometry trees'' which correspond to the hierarchy of volumes a detector geometry can be composed of, and to allow to identify the position of individual solids, as well as to describe the materials they are made of. Being pure XML, GDML can be universally used, and in particular it can be considered as the format for interchanging geometries among different applications. In this paper we will present the current status of the development of GDML. After having discussed the contents of the latest GDML schema, which is the basic definition of the format, we will concentrate on the GDML processors. We will present the latest implementation of the GDML ''writers'' as well as ''readers'' for either Geant4 [2], [3] or ROOT [4], [10].

  13. Lamb wave behavior in bridge girder geometries

    NASA Astrophysics Data System (ADS)

    Oppenheim, I. J.; Greve, D. W.; Tyson, N. L.

    2006-03-01

    Lamb waves in plates and in cylindrical pipes have been the subject of extensive study, largely because they propagate great distances with little attenuation, and can therefore be used to detect flaws. In this paper we report finite element simulations and experimental studies of Lamb waves in steel bridge girder geometries. In our studies the Lamb waves are generated by PZT wafer-type transducers mounted on the girder web, driven by a windowed sinusoidal pulse; the pulse center frequency is chosen to yield a frequency-thickness product of roughly 1 MHz-mm, at which the group velocities of the S0 and A0 waves are well separated, and at which waves in higher modes are theoretically absent. Transient dynamic finite element simulations, both in 2D and in 3D, were performed using FEMLAB and ABAQUS. The simulations show that transmission at the web-flange joint creates guided waves in the flanges that travel at different velocities from the Lamb waves in the web, and that reflection at the web-flange joint creates a largely straight-crested wavefront for the Lamb waves in the web remote from the source. Simulation studies also illustrate the acoustic influence of plate girder transverse stiffeners, which is observed to be relatively small. A welded steel plate girder laboratory specimen was fabricated with proportions typical of highway bridge members, at approximately half-scale. The web height is 920 mm and thickness is 3.2 mm, for a representative height-thickness ratio of 288; the flange width is 100 mm and thickness is 6.4 mm, for a representative width-thickness ratio of 16. Small PZT transducers, roughly 6.4 x 6.4 x 0.6 mm, excited at less than 10 V, produce ample signals. We compare simulation results and experimental measurements for Lamb wave illumination of the plate girder segment. We also discuss the detection of cracks, simulated experimentally by saw cuts of varying dimensions in the laboratory girder specimen.

  14. Stepped Hydraulic Geometry in Stepped Channels

    NASA Astrophysics Data System (ADS)

    Comiti, F.; Cadol, D. D.; Wohl, E.

    2007-12-01

    Steep mountain streams typically present a stepped longitudinal profile. Such stepped channels feature tumbling flow, where hydraulic jumps represent an important source of channel roughness (spill resistance). However, the extent to which spill resistance persists up to high flows has not been ascertained yet, such that a faster, skimming flow has been envisaged to begin at those conditions. In order to analyze the relationship between flow resistance and bed morphology, a mobile bed physical model was developed at Colorado State University (Fort Collins, USA). An 8 m-long, 0.6 m-wide flume tilted at a constant 14% slope was used, testing 2 grain-size mixtures differing only for the largest fraction. Experiments were conducted under clear water conditions. Reach-averaged flow velocity was measured using salt tracers, bed morphology and flow depth by a point gage, and surface grain size using commercial image-analysis software. Starting from an initial plane bed, progressively higher flow rates were used to create different bed structures. After each bed morphology was stable with its forming discharge, lower-than-forming flows were run to build a hydraulic geometry curve. Results show that even though equilibrium slopes ranged from 8.5% to 14%, the reach-averaged flow was always sub-critical. Steps formed through a variety of mechanisms, with immobile clasts playing a dominant role by causing local scouring and/or trapping moving smaller particles. Overall, step height, step pool steepness, relative pool area and volume increased with discharge up to the threshold when the bed approached fully- mobilized conditions. For bed morphologies surpassing a minimum profile roughness, a stepped velocity- discharge relationship is evident, with sharp rises in velocity correlated with the disappearance of rollers in pools at flows approaching the formative discharge for each morphology. Flow resistance exhibits an opposite pattern, with drops in resistance being a function

  15. Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster.

    PubMed

    Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf

    2015-11-28

    We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided. PMID:26503611

  16. An Analysis of How and Why High School Geometry Teachers Implement Dynamic Geometry Software Tasks for Student Engagement

    ERIC Educational Resources Information Center

    Nirode, Wayne

    2012-01-01

    This study examined teachers' use of student tasks involving dynamic geometry software, in which a figure is constructed then altered while maintaining its constructed properties. Although researchers, professional organizations, and policy makers generally have been proponents of dynamic geometry for instruction, there is little research…

  17. Teachers' Scaffolding of Students' Learning of Geometry While Using a Dynamic Geometry Program

    ERIC Educational Resources Information Center

    Dove, Anthony; Hollenbrands, Karen

    2014-01-01

    This study examined the scaffolds that three high school mathematics teachers provided to their geometry students as they used technology to explore geometric ideas. Teachers often used structured activities using a dynamic geometry program and provided significant emotive feedback while students worked through the tasks. This provided…

  18. A Vector Approach to Euclidean Geometry: Inner Product Spaces, Euclidean Geometry and Trigonometry, Volume 2. Teacher's Edition.

    ERIC Educational Resources Information Center

    Vaughan, Herbert E.; Szabo, Steven

    This is the teacher's edition of a text for the second year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

  19. Geometry Teaching--Geometrieunterricht. Conference on the Teaching of Geometry (Helsinki, Finland, August 1-4, 1989). Research Report 74.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki, Ed.

    This report contains conference papers on geometry teaching. There were five plenary talks given and a review of Hungarian geometry teaching. The plenary talks addressed background theories of the psychology of learning such as constructivism, perceptional psychology, and motivational psychology. The themes of the 21 short talks were on a varied…

  20. The relationship between strain geometry and geometrically necessary dislocations

    NASA Astrophysics Data System (ADS)

    Hansen, Lars; Wallis, David

    2016-04-01

    The kinematics of past deformations are often a primary goal in structural analyses of strained rocks. Details of the strain geometry, in particular, can help distinguish hypotheses about large-scale tectonic phenomena. Microstructural indicators of strain geometry have been heavily utilized to investigate large-scale kinematics. However, many of the existing techniques require structures for which the initial morphology is known, and those structures must undergo the same deformation as imposed macroscopically. Many deformed rocks do not exhibit such convenient features, and therefore the strain geometry is often difficult (if not impossible) to ascertain. Alternatively, crystallographic textures contain information about the strain geometry, but the influence of strain geometry can be difficult to separate from other environmental factors that might affect slip system activity and therefore the textural evolution. Here we explore the ability for geometrically necessary dislocations to record information about the deformation geometry. It is well known that crystallographic slip due to the motion of dislocations yields macroscopic plastic strain, and the mathematics are established to relate dislocation glide on multiple slip systems to the strain tensor of a crystal. This theoretical description generally assumes that dislocations propagate across the entire crystal. However, at any point during the deformation, dislocations are present that have not fully transected the crystal, existing either as free dislocations or as dislocations organized into substructures like subgrain boundaries. These dislocations can remain in the lattice after deformation if the crystal is quenched sufficiently fast, and we hypothesize that this residual dislocation population can be linked to the plastic strain geometry in a quantitative manner. To test this hypothesis, we use high-resolution electron backscatter diffraction to measure lattice curvatures in experimentally deformed

  1. Flexible intuitions of Euclidean geometry in an Amazonian indigene group.

    PubMed

    Izard, Véronique; Pica, Pierre; Spelke, Elizabeth S; Dehaene, Stanislas

    2011-06-14

    Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ~180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. PMID:21606377

  2. Exact helical reconstruction using native cone-beam geometries

    NASA Astrophysics Data System (ADS)

    Noo, Frédéric; Pack, Jed; Heuscher, Dominic

    2003-12-01

    This paper is about helical cone-beam reconstruction using the exact filtered backprojection formula recently suggested by Katsevich (2002a Phys. Med. Biol. 47 2583-97). We investigate how to efficiently and accurately implement Katsevich's formula for direct reconstruction from helical cone-beam data measured in two native geometries. The first geometry is the curved detector geometry of third-generation multi-slice CT scanners, and the second geometry is the flat detector geometry of C-arms systems and of most industrial cone-beam CT scanners. For each of these two geometries, we determine processing steps to be applied to the measured data such that the final outcome is an implementation of the Katsevich formula. These steps are first described using continuous-form equations, disregarding the finite detector resolution and the source position sampling. Next, techniques are presented for implementation of these steps with finite data sampling. The performance of these techniques is illustrated for the curved detector geometry of third-generation CT scanners, with 32, 64 and 128 detector rows. In each case, resolution and noise measurements are given along with reconstructions of the FORBILD thorax phantom.

  3. Modeling of metal interaction geometries for protein-ligand docking.

    PubMed

    Seebeck, Birte; Reulecke, Ingo; Kämper, Andreas; Rarey, Matthias

    2008-05-15

    The accurate modeling of metal coordination geometries plays an important role for structure-based drug design applied to metalloenzymes. For the development of a new metal interaction model, we perform a statistical analysis of metal interaction geometries that are relevant to protein-ligand complexes. A total of 43,061 metal sites of the Protein Data Bank (PDB), containing amongst others magnesium, calcium, zinc, iron, manganese, copper, cadmium, cobalt, and nickel, were evaluated according to their metal coordination geometry. Based on statistical analysis, we derived a model for the automatic calculation and definition of metal interaction geometries for the purpose of molecular docking analyses. It includes the identification of the metal-coordinating ligands, the calculation of the coordination geometry and the superposition of ideal polyhedra to identify the optimal positions for free coordination sites. The new interaction model was integrated in the docking software FlexX and evaluated on a data set of 103 metalloprotein-ligand complexes, which were extracted from the PDB. In a first step, the quality of the automatic calculation of the metal coordination geometry was analyzed. In 74% of the cases, the correct prediction of the coordination geometry could be determined on the basis of the protein structure alone. Secondly, the new metal interaction model was tested in terms of predicting protein-ligand complexes. In the majority of test cases, the new interaction model resulted in an improved docking accuracy of the top ranking placements. PMID:18041759

  4. Multigrid Methods for Aerodynamic Problems in Complex Geometries

    NASA Technical Reports Server (NTRS)

    Caughey, David A.

    1995-01-01

    Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

  5. Nonmonotonic thermal Casimir force from geometry-temperature interplay.

    PubMed

    Weber, Alexej; Gies, Holger

    2010-07-23

    The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate geometries develops a nonmonotonic behavior already in the simple case of a fluctuating Dirichlet scalar. In particular, the attractive thermal force can increase for increasing distances below a critical temperature. This anomalous behavior is triggered by a reweighting of relevant fluctuations on the scale of the thermal wavelength. The essence of the phenomenon becomes transparent within the worldline picture of the Casimir effect. PMID:20867823

  6. Five Dimensional Minimal Supergravities and Four Dimensional Complex Geometries

    SciTech Connect

    Grover, Jai; Gutowski, Jan B.; Herdeiro, Carlos A. R.; Sabra, Wafic

    2009-05-01

    We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant {lambda} 0) the solutions are determined in terms of a hyper-Kaehler base space; in the gauged case ({lambda}<0) the complex geometry is Kaehler; in the de Sitter case ({lambda}>0) the complex geometry is hyper-Kaehler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.

  7. Determination of electron-nucleus collisions geometry with forward neutrons

    SciTech Connect

    Zheng, L.; Aschenauer, E.; Lee, J. H.

    2014-12-29

    There are a large number of physics programs one can explore in electron-nucleus collisions at a future electron-ion collider. Collision geometry is very important in these studies, while the measurement for an event-by-event geometric control is rarely discussed in the prior deep-inelastic scattering experiments off a nucleus. This paper seeks to provide some detailed studies on the potential of tagging collision geometries through forward neutron multiplicity measurements with a zero degree calorimeter. As a result, this type of geometry handle, if achieved, can be extremely beneficial in constraining nuclear effects for the electron-nucleus program at an electron-ion collider.

  8. The standard model and beyond in noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Schelp, Richard Charles

    2000-11-01

    Noncommutative geometry and the formulation of the standard model within it is reviewed. The phrasing within noncommutative geometry of a model of particle physics based on S(U(2) × U(3)) is attempted and found to be incompatible with the mathematical structure. Noncommutative geometry versions of unified theories based on SU(15) and SU(16) are found not to yield the necessary spontaneous symmetry breaking. An extension of the standard model which includes right-handed neutrinos (and no additional fermions) is shown to be compatible with Poincaré duality only if the number of right- handed neutrinos is not equal to three.

  9. Observing the geometry of warped compactification via cosmic inflation.

    PubMed

    Shiu, Gary; Underwood, Bret

    2007-02-01

    Using Dirac-Born-Infeld inflation as an example, we demonstrate that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background. We compute cosmic microwave background observables for Dirac-Born-Infeld inflation in a generic class of warped throats and find that the results (such as the sign of the tilt of the scalar perturbations and its running) depend sensitively on the precise shape of the warp factor. In particular, we analyze the warped deformed conifold and find that the results can differ from those of other warped geometries, even when these geometries approximate well the exact metric of the warped deformed conifold. PMID:17358841

  10. Nonmonotonic Thermal Casimir Force from Geometry-Temperature Interplay

    SciTech Connect

    Weber, Alexej; Gies, Holger

    2010-07-23

    The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate geometries develops a nonmonotonic behavior already in the simple case of a fluctuating Dirichlet scalar. In particular, the attractive thermal force can increase for increasing distances below a critical temperature. This anomalous behavior is triggered by a reweighting of relevant fluctuations on the scale of the thermal wavelength. The essence of the phenomenon becomes transparent within the worldline picture of the Casimir effect.

  11. Indentation Tests Reveal Geometry-Regulated Stiffening of Nanotube Junctions.

    PubMed

    Ozden, Sehmus; Yang, Yang; Tiwary, Chandra Sekhar; Bhowmick, Sanjit; Asif, Syed; Penev, Evgeni S; Yakobson, Boris I; Ajayan, Pulickel M

    2016-01-13

    Here we report a unique method to locally determine the mechanical response of individual covalent junctions between carbon nanotubes (CNTs), in various configurations such as "X", "Y", and "Λ"-like. The setup is based on in situ indentation using a picoindenter integrated within a scanning electron microscope. This allows for precise mapping between junction geometry and mechanical behavior and uncovers geometry-regulated junction stiffening. Molecular dynamics simulations reveal that the dominant contribution to the nanoindentation response is due to the CNT walls stretching at the junction. Targeted synthesis of desired junction geometries can therefore provide a "structural alphabet" for construction of macroscopic CNT networks with tunable mechanical response. PMID:26618517

  12. Variable geometry inlet design for scram jet engine

    NASA Technical Reports Server (NTRS)

    Guinan, Daniel P. (Inventor); Drake, Alan (Inventor); Andreadis, Dean (Inventor); Beckel, Stephen A. (Inventor)

    2005-01-01

    The present invention relates to an improved variable geometry inlet for a scram jet engine having at least one combustor module. The variable geometry inlet comprises each combustor module having two sidewalls. Each of the sidewalls has a central portion with a thickness and a tapered profile forward of the central portion. The tapered profile terminates in a sharp leading edge. The variable geometry inlet further comprises each module having a lower wall and a movable cowl flap positioned forward of the lower wall. The movable cowl flap has a leading edge and the leading edges of the sidewalls intersect the leading edge of the cowl flap.

  13. Nozzle and wing geometry effects on OTW aerodynamic characteristics

    NASA Technical Reports Server (NTRS)

    Vonglahn, U.; Groesbeck, D.

    1976-01-01

    The effects of nozzle geometry and wing size on the aerodynamic performance of several 5:1 aspect ratio slot nozzles are presented for over-the-wing (OTW) configurations. Nozzle geometry variables include roof angle, sidewall cutback, and nozzle chordwise location. Wing variables include chord size, and flap deflection. Several external deflectors also were included for comparison. The data indicate that good flow turning may not necessarily provide the best aerodynamic performance. The results suggest that a variable exhaust nozzle geometry offers the best solution for a viable OTW configuration.

  14. A Combinatorial Geometry Code System with Model Testing Routines.

    Energy Science and Technology Software Center (ESTSC)

    1982-10-08

    GIFT, Geometric Information For Targets code system, is used to mathematically describe the geometry of a three-dimensional vehicle such as a tank, truck, or helicopter. The geometric data generated is merged in vulnerability computer codes with the energy effects data of a selected @munition to simulate the probabilities of malfunction or destruction of components when it is attacked by the selected munition. GIFT options include those which graphically display the vehicle, those which check themore » correctness of the geometry data, those which compute physical characteristics of the vehicle, and those which generate the geometry data used by vulnerability codes.« less

  15. Accurate Excited State Geometries within Reduced Subspace TDDFT/TDA.

    PubMed

    Robinson, David

    2014-12-01

    A method for the calculation of TDDFT/TDA excited state geometries within a reduced subspace of Kohn-Sham orbitals has been implemented and tested. Accurate geometries are found for all of the fluorophore-like molecules tested, with at most all valence occupied orbitals and half of the virtual orbitals included but for some molecules even fewer orbitals. Efficiency gains of between 15 and 30% are found for essentially the same level of accuracy as a standard TDDFT/TDA excited state geometry optimization calculation. PMID:26583218

  16. Loewner's conjecture, the Besicovitch barrel, and relative systolic geometry

    SciTech Connect

    Babenko, I K

    2002-04-30

    The paper is devoted to relative systolic geometry on a compact manifold with boundary. Sufficient conditions ensuring the intersystolic rigidity or intersystolic softness of such manifolds are analyzed. Several open questions are formulated.

  17. Using Children's Literature to Teach Geometry and Measurement.

    ERIC Educational Resources Information Center

    Meconi, L. J.; Moss, Barbara

    1991-01-01

    Discusses selected children's literature dealing with geometry and measurement concepts. Suggests activities for grades three through six to be used as part of a learning center or to be completed in cooperative learning groups. (MG)

  18. 8. General view of truss geometry at center of span ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    8. General view of truss geometry at center of span from lower parking lot, looking northwest - Lower Rollstone Street Bridge, Spanning Nashua River on Rollstone Street, Fitchburg, Worcester County, MA

  19. Elastic Geometry and Storyknifing: A Yup'ik Eskimo Example.

    ERIC Educational Resources Information Center

    Lipka, Jerry; Wildfeuer, Sandra; Wahlberg, Nastasia; George, Mary; Ezran, Dafna R.

    2001-01-01

    Introduces elastic geometry, or topology, into the elementary classroom through the study of connecting the intuitive, visual, and spatial components of storyknifing as well as other everyday and ethnomathematical activities. (ASK)

  20. Unit cell geometry of 3-D braided structures

    NASA Technical Reports Server (NTRS)

    Du, Guang-Wu; Ko, Frank K.

    1993-01-01

    The traditional approach used in modeling of composites reinforced by three-dimensional (3-D) braids is to assume a simple unit cell geometry of a 3-D braided structure with known fiber volume fraction and orientation. In this article, we first examine 3-D braiding methods in the light of braid structures, followed by the development of geometric models for 3-D braids using a unit cell approach. The unit cell geometry of 3-D braids is identified and the relationship of structural parameters such as yarn orientation angle and fiber volume fraction with the key processing parameters established. The limiting geometry has been computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for 3-D braided preforms. This identified unit cell geometry can be translated to mechanical models which relate the geometrical properties of fabric preforms to the mechanical responses of composite systems.